Years ago i had one of those old fashioned avocado green "dial-a-matic" sharpeners. I miss that silly little thing very much, it just vanished one day. Right now i use a fiskars sharpener and it works ok on my fabric scissors that somehow always make it in with the paper cutting scissors. I've been watching thrift stores to find another one of those sharpeners but for now i ordered a new pair of scissors that i have warned the family several times will be fabric only.
It is not a myth about using scissors for one purpose and not mixing them up. When i was a kid i used my moms fancy hair cutting scissors for a craft project and the hell she went through getting them sharpened (expensive) left quite an impression on me. I've also noticed that i can't use general purpose scissors to clip coupons after my daughter has used them to cut construction paper so now we have several pairs of scissors around the house meant for specific tasks.