Fixing crummy kitchen drawers
I am in the process of refurbishing my kitchen cabinets (painting mostly, some repairs, some storage enhancements, some trim). One of the repairs I need to do is to the drawers. They are crummy. Literally. No dovetails, miters here ... badly made, old, crumbling plywood drawers. I'm tired of having sawdust fall on my dishes. See pic and you will know what I mean.
I have a full array of carpentry tools. My Dad wanted to make furniture, so we had all been buying him nice tools for holidays for a few years. Unfortunately, he died (6 years ago) before he even got the chance to use many of them. I know how to use the compound miter saw, scroll saw, jig saw, drill, and hand tools. I am guessing that a router would be the right tool to clean up the edges on these drawers. I have a router, but I've never tried it out. I do have scrap wood to practice on.
I don't know that I have the right bit or not. My plan is to even out the edges and apply some sort of laminate/veneer edging, though I'm not sure what. Better ideas, advice about what type of bit to use, what sort of edge covering to use, good tutorials all gratefully accepted. I'm hoping not to rebuild them entirely, though that is possibly the right answer.