Can I rave about Islabikes please? Bikes designed for kids with kid-friendly components eg. brakes their hands can actually use, kid-sized pedals. Don't take my word for it, just search the internet for children's bike reviews.
www.islabikes.co.uk
They do deliver to Switzerland and even with import duty, their prices are better than many bikes bought here. They also say that they will buy your old Islabike when your child outgrows it and you buy a new Islabike, although I don't know anyone who has done this.
Our son had no problems going from a balance bike to Islabike when he was 4 years old (on his 4th birthday). I would definitely agree, stabilisers are not necessary.
This is the one he has -
http://www.islabikes.co.uk/bike_pages/cnoc16.html
Our neighbours bought an all-singing, all-dancing, expensive bike for their son and he could not ride it. He tried on my son's Islabike and instantly cycled away. Literally, although stopping took a bit longer to master!
We are just about to buy a bigger Islabike for my son's birthday in September, so if you want to buy a Cnoc 16, give me a pm!