Cut a flat, unfitted mattress pad down to size and sew ready made seam binding around the edges. Reuse the old corner elastic on the newly resized corners. No one is going to pull the sheets up to inspect your stitching.
Just remember sewing a sheet is also really very easy. To make the sheet smaller you make a cut at the bottom edge of the sheet at the size you want and start tearing. Fabrics tear in a straight line along the weave. You will only have two sides to modify
You will need to cut the folded over head of the sheet part in line with the torn edge. As far as turning the edges of the sheet under for that narrow hemmed edge that is pretty easy too as they make a rolled hem presser foot that does that work for you. One of those might even have come with your sewing machine. Here is a tutorial about it.
Flawless Finish: How to Use a Rolled Hem Presser Foot
If you want a corner on a bottom sheet that is gathered.... Use a plate as a template for the curve and draw the line on, cut and be sure to hem it with your rolled hem edge foot right along with the rest of the sheet's modified edges. Then stretch out tight some elastic along the curved line. Pin the elastic in place every few inches and stretch it back out flat tugging on it while you sew. Sew the elastic on using a zig zag stitch.