I don't like the doubles tournaments when it's shoot till you miss instead of alternating shots, it's not relaly a doubles tournament then since you can guarantee a win when the better player plays instead of having to deal with a possible miss or bad position by the weaker player in every game.
I don't think you need to change your game at all, I mean if you were by yourself, you'd play the same way to try to win, so play the same way. If you are worried that you'll let down or dissapoint your partner, don't, if you have to think that way, you picked the wrong partner. And it will likely just mess you up by adding 4 more things you have in your head aside from just the shot you are shooting.
I played in a doubles tournament where it's shoot till you miss, never again. The bad player was pretty bad, but she would invarabily just play a safe to try to get the better guy to the table again to run out, or get really luck and leave me or my partner (who was my son), no shot. If it was singles, even after the safe, it would then be on HER to run out, so she'd still need to shoot the balls in instead of having someone 2 levels over her take over. If it was doubles, then they have to deal with her playing bad shape or missing the shot every other shot. As it was with shoot till you miss, there was none of what you'd see in a true doubles tournament. She'd shoot a shot, miss, then we'd go, if we missed or were hooked and left an open shot after a kick, the good player won the game for them. Boring to play that way and not in the spirit of doubles at all.
Plus it totally messes with your rhythm and thinking waiting to shoot extra turns if you don't shoot alternate shots.