To fuse or not to fuse the rings

Not sure if this is exactly right forum. Please let me know if it is not. Should I fuse rings? Do they just tac a few points together or fully solidify the rings together? I have an enhancer my engagement ring sits in and they are 2 different sizes. I'm thinking I'd have the engagement ring sized up a tad to match the enhancer and so that with the greater thickness, won't squeeze as tightly. It's not uncomfortable or anything but I would love of the rings could sit flush. I can't shrink the enhancer any more due to the channel. Thoughts?