There is no need to do nuthin. No stretching no pulling no nothing. The 7 speed cassette is completely fine. Just add 7 speed brifters. You have a choice of four 7 speed brifters:
RSX A410
Sora 3300
Tourney A070
Micro-new r7
Those last two are still available brand new. Brifters and dual pivot brakes will transform your bike.