Altering a backless swimsuit?

I recently bought a backless swimsuit which fits great but tents slightly at the back and exposes the small of my back and my waist. It fits just fine when I pinch around the sides - it is discontinued so this is the one size only . It really doesn’t expose too much but ideally I would like to take it in to sit flush to my skin. I’ve taken in tops before with my very very basic sewing skills by just flipping it inside out and doing a zig-zag stitch with my sewing machine and cutting off the excess, but I’ve never dealt with nylon , how do I go about taking it in? and am I okay to just use any thread?