Paint removal  

The old-fashion way, Daniel.
Hire a pro.
Otherwise, remove the upholstery and try a test with one of the less aggressive strippers like soy-based. Escalate from there as results warrant.

Thank you as always, tktoo
Will that remove water-based paint too?

I've always just gone straight to
time-tested methylene chloride strippers due to my impatient nature, (and, yes, it's a personality flaw) but I've heard good reports about soy strippers.
I think you're right about avoiding dipping bent laminations.

Smart Strip by Peel Away is...
Smart Strip by Peel Away is a water based paint remover. I've used it before with great results.

Peel Away
I haven't used their products for latex, but their products for old oil-based trim paint (I've used it on old oil-based paint on baseboards and trim moulding) is wonderful. Talk about a time saver.

no advice on paint
but the chair is indeed by Hans Olsen

Could the paint have been original?
Seems very even to be done by an amateur.
I would love to see a pic of the sofa!

Bought the Peelaway
Results to follow.
Definitely been painted (badly) but the good thing is that I can scrape off the paint with my nail so it should come off easily.
Bj, I got a set: 2 chairs, sofa and a coffee table. I've seen a set (see photo) in a dark stain which look lovely. Although the stain does not look original, it sure does look nice
http://www.1stdibs.com/furniture/seating/settees/pair-of-bent-plywood-se...