Big Alterations?

You'd be surprised what seamstresses can do! I've seen them completely transform a dress! I think your off the shoulder straps will be a walk in the park for them. I'm not altering my straps but i am altering the front of my dress. It's currently a very deep V and we are adding lace appliques to the entire front and neck line for extra coverage that I want.

I added detachable off the shoulder straps, lowered the back of my dress, hemmed & took it in, and sewed my fiance's nametape to the inside. My dress originally had no straps!

So as an amateur seamstress making the straps be over the shoulder would be easy if you can currently push the straps off or inside the dress and it still stays up. If it doesn't have enough structure to do that then it a much greater task to make sure moving the straps won't cause a wardrobe malfunction.

If the dress has enough structure to stay up on its own (like a strapless dress), it should be an easy fix!

If the straps are what's keeping the dress from falling down, it would be more difficult, but not necessarily impossible.