Yup

And they have packs of wet-or-dry sandpaper that you'll need, and it's cheaper than LHS prices by far.

I second the idea that you just sand the present finish not use paint remover, but would like to add some details. If you hand sand the present finish with wet paper, you can easily produce a very good (and clean base for your paintjob. I'd start with 320 or 400 paper and if you do it right one sanding should be good enough. It's not hard to sand just enough if you're careful. Put a drop of dish soap into the water and keep the surface wet and you wash the sucker down as you prepare the surface. Dry it off, tack rag it, let it dry overnight, and paint it.

Wiping it down beforehand with lacquer thinner is a good idea but do it outside and let it sit out there awhile afterwards as well. That stuff is really strong. You might consider denatured alcohol for the same job. It's slightly less aeromatic (and toxic) and does a good cleaning job. If you use the thinner too liberally around joints and cracks, you might loosen up old glues that might not stiffen back up so go lightly around any cracks you find. Use plenty of paper towels. You want the liquid to lift old oil and it will, but it won't remove it unless you hose it off, so use the paper towels often and keep using a clean dry one. If you just wipe the plane down with one rag all you've done is spread the oil evenly over the entire surface.

Oh yeah... I said "hand sanding" but you really want to use a sanding block. Using one by hand does wonders to the old surface, especially if the previous paintjob wasn't real smooth. Without the block you do some smoothing, but it's not half as flat as the block will give you.