Bring in guys who throw the ball down the middle with movement at 95+. Works well in HS ball.
Seriously, each pitcher has to make their own adjustments to the umpire and the team they're facing on a game by game basis. Some teams will be swinging the bat and as long as you aren't all out nibbling it won't really matter if the strike zone is tight. Some teams are trying to work the count and in that case you need to just pour it down the middle. It also varies from hitter to hitter. One treats the punch hitter differently than the home run hitter.
We ran into an umpire with a tight zone this past weekend. Both starters had dominated the previous week with a different umpire. This time around with the tighter strike zone both starters struggled a bit and gave up some runs, but neither was walking anyone until each one got tired in their last inning of work. When the relievers came in the game got out of hand with walks, etc. pretty quickly. In other words, if you pitch your game and grind it out when you're facing a tight zone you should be OK. Either the other pitcher is going to have to do the same thing so you're even or they won't be able to handle it and you've got the advantage. Look at a tight strike zone as an advantage. It won't help your ERA but it will help you get a win if you do your job.