Does your opponent still get to choose if they want to board if you choose not to?
Yes. Blade hits count as ramming, so standard boarding rules apply to each.
The player with the Switchblade can decide the order those rams occur, but once a ramming is resolved, they can’t can’t prevent a boarding if the opponent wants to do it.
For timing purposes, it goes Ram/Board 1, Ram/Board 2, Ram/Board 3, etc. (NOT Ram 1, Ram 2, Ram 3, Board 1, Board 2, Board 3…)