You can use ANY board, for a downwinder
If you want to win, you are probably best off with a board that glides well, meaning a medium raceboard with smaller fins.
Can go deeper thus better VMG.
If very very choppy/waves and difficult conditions, a light wind waveboard, strapped, can also be good.
A TT no problem either, if not lightwind, but your stance is a bit awkward with one leg bent, but if you change tack often, you dont get sore/tired.
A foilboard can also be used, because it causes the least stress because of no bumps nor kitepull - but I dont know if slower than a raceboard on a downwind tack ?
At least not as easy for most....
If you are going on a deep downwinder, same tack - I would stay away from the twintip because of the odd stance and cramps can occur