Why does everyone give jwm such a bad rap? Yes, jwm can do that. Enter this in your .jwmrc for whatever application you want on every window (and with any other options -- including two you can probably do without):
Add that just below the </RootMenu> tag and then it should work when you restart jwm. Sticky puts it on every desktop. You can take out the options for border and title if you want window decorations and the nolist option keeps it out of the task list. You can also add an option of layer if you want to raise or lower it above everything else (so it's more or less tied to your background than floating app windows).