Buy something else.

That's going to be tough because it looks like the drawers have curved faces. Someone good in woodworking could probably do it but who knows how much that would cost.

It doesn't look tall enough to use. Not only o you need fronts, but the drawers have to be altered to receive the plumbing. You might need to change the runner to full extension glides on the sides of the drawers.

I wouldn't hide the top shelves. I would actually use those top open drawers to put pretty décor. flowers maybe orchids in small vases. you could put folded pretty hand towels. there is a lot you can do to make it pretty. covering it up will wont make the bathroom look pretty.