For convex, I do sandpaper on mousepad followed by strops. I use Flexxx Strops loaded with Bark River compound.
For scandi, here's a really cheap sharpening system I put together that's similar to my convex system. This is not my original idea and I take no credit for it - I just wanted to share the ideas I've gathered.
I picked up a cheap (about $5) 12"x12" granite tile from Lowes to use as the base. The tile is perfectly (as far as I can tell) flat. You could also use a piece of plate glass or a glass table top.
Other supplies used are a no-slip drawer liner to put under the granite tile to keep it from slipping on the table, spray adhesive for attaching the sandpaper to the tile and various grits (220, 400, 600, 800, 1000, 2000) of automotive wet/dry sandpaper from an auto parts store.
If the blade needs serious work, I'll go all the way back to 220 and work up from there. Normally however when they just need a touchup I'll start at 600 or 800. I cut down the larger sheets of sandpaper into 3 2/3" x 9" strips.
Attach the sandpaper to the tile with the spray adhesive. I can usually lift and attach a few sheets before needing to reapply the adhesive. I use Mineral Spirits to clean the tile in order to make sure the adhesive doesn't build up.
I pull the knife across the paper similar to what you'd do on a strop instead of pushing it like you would on a stone. It might work fine pushing, I just don't want to take a chance on cutting into the paper.
Finally, depending on how hard I plan on using the knife in question, I'll put on a VERY fine micro bevel with a couple swipes on the Sharpmaker or a strop.
My only real cost was the granite tile as I already use the sandpaper for sharpening convex knives on a mousepad and the other supplies I already had around the house.