I would!! Personally don't connect past feelings with these type things.
If he wants you to have it coz grandma was special to him that's all I'd need.
Especially since things are amicable between him & her, and you & her.
Money is tight for most of us, for now give it a try & when you guys get more stable financially then, if you need to rethink things.

Congrats & best of luck to you!

PS. got my first wedding set from a pawn shop & still means the world to me. It's small, simple & I wore it for 18yrs. Last year pulled out ex-hubs diamond (from back in 1980's) & had it set in my late MIL's band. Hubby is honored & thinks it's a beautiful ring.