First of all, the airline is called Helvetic, and it’s a wet lease flight, so it’s as if you’d be flying on Swiss. For that leg you. can credit to any *A program.

As for Edelweiss you can only credit to Miles&More or UA and not any other *A program including Eurobonus.
Edelweiss is a daughter/sister company of Swiss, but not a member of *A, but despite that you only earn miles on M&M when booked on the LX codeshare number.