The 33-year-old Finn landed at the Liberty Stadium towards the end of the January transfer window on the latest leg of an interesting life.
War and transition into a new way of life in a different country was just the beginning of a journey which has led to the striker becoming a household name in two different corners of Europe - his native Kosovo and adopted homeland Finland.
Not many people are aware of Kuqi's early life in Kosovo, an autonomous province between Albania and Serbia, where he spent the first 11 years of his life.
But as one of the central points of the bloody Balkans conflicts in the early 1990's, where the ethnic Albanians - of which the Kuqi family belongs - were in dispute with their Serbian rulers which eventually led to Nato's war with Kosovo.
"We left Kosovo after one of my brothers called up to the army," recalls Kuqi, sipping a coffee before braving the Welsh elements for a training session with his new team mates.
"My parents decided that it would be safer to leave for his and our safety."
Finland was the preferred destination for the Kuqi family where his mother's sister had already moved a couple of months before.
And after initially spending the first couple of weeks in the Finnish capital Helsinki they moved to the eastern town of Mikkeli "where everything started."
As you could image the transition into Nordic life wasn't easy to start with; the language barrier proved to be most difficult, while Kuqi even had to wait a year before entering the Finnish education system.
"When you're young and to move away from your home, friends and family it's always going to be difficult," he said.
"And I didn't really know anything about the place we were moving to.
"It was difficult, especially the language and the culture, it was all new to me. As a kid you can adapt quite quickly but it was still hard - you don't speak the language, you don't know what's going on.
"When we arrived in about October time school had already started so I went a year before even starting school.
"But when I did start it was quite funny thinking back, you'd have all of the kids sitting there listening to the teacher and I didn't have a clue what they were on about.
"And by not knowing the language it was made even harder to make friends."
It took Shefki the best part of two years to pick up the Suomi dialect, during which time he started playing football.
But even then his team mates failed to take to him instantly as he couldn't speak the lingo, though he will be extremely thankful to the country that gave him his break in the beautiful game.
It was at Mikkelin Palloilijat where he'd started his professional career in '95 before switching to HJK Helsinki where, in three seasons, won a Veikkausliiga (premier division) title, as well as a Finnish Cup and League Cup winners medals.
The bright lights of English football came calling at the turn of the century with a move to then Championship side Stockport County handing him his chance, one that has spanned almost 10 years, with the exception of a brief spell in Germany prior to his first move to Wales.
However he will always be debted to Finland for the chance he was giving in becoming a professional footballer.
"I will always be thankful to that country," he said with a smile on his face.
"That's where I started to make my name in football. I've also been involved with the national team there for the last 10 years and when I am called up always look forward to playing for them.
"Every time I play for them I try to do my best to help the team; I haven't started as many games I've wanted to, but I have 60 caps and am always proud to play for them."
Despite growing up in Finland, where his family still lives today, he will never forget his Kosovan roots.
Kuqi still has family there, as does wife Xhyljeta, a singer - who is expecting the couples first child - and both will go to the Baltic state every summer to visit relatives.
After originally leaving Kosovo it was 10 years before he was able to go back following the end of the conflict, and even when he did return to his home village, affectionately branded 'Kuqi town' for its dense population of residents baring the famous name, nobody even recognised him at first.
"Obviously in the 10 years I was away I had grown up a lot and when I went back for the first time nobody recognised me, not even my own family.
"I knew who they were and when I told them there was a lot of emotion. It was a different place but it's always nice to go back to where you came from."
From Kosovo to Finland to England and, via Germany, the striker has now ended up in Wales with the task of helping Swansea City achieve their dream of Premier League football.
After making his first two appearances from the bench against Coventry and Preston he was handed a full debut at former employers Crystal Palace four days ago.
Kuqi made an instant impact with the winner just 14 minutes into the Selhurst Park contest to become an instant hit with the Swansea faithful.
But even before getting off the mark he's been delighted with the welcome he's had in south west Wales, while also getting a surprise at what his new home is actually like.
"I didn't know what to expect at first, especially with Swansea being so far away.
"But Ipswich (where he played between 2003 and 2005 and again in 2008) is a similar place and I had a very good time there. If I enjoy my football it doesn't matter where I am.
"But Swansea is a nice place, it's much bigger than I thought it was and there are a lot of beautiful places here, loads of nice beaches and places you can go.
"Both my wife and I are feeling really positive about our time here, and I know that when I get my first goal (which he scored against Palace) I will start scoring more and hopefully I can help the team."
He added: "Not just outside of the club but inside the club the people are very nice. I've had a very warm welcome.
"And when I've been out and about people have come up to me in the town to say hello and welcome me. I'm confident that I will be able to please them by scoring goals and helping the team."
Kuqi opted against celebrating his midweek strike out of respect for his former club, let's hope that he'll be keeping his renowned and appropriately named 'Swan Dive' for another special occasion - today would be nice.