The 133 has enough float for you, it is just a matter of where the float is located. As Roger noted, the 133’s nose is much slimmer then the rest of the board so much less stable up there and a change in tacking technique is needed. Another option to Roger’s technique of tacking shortboards is to go around the mast before the nose crosses the wind to the new tack and backwinding the sail. This method works because the board is still moving so when you step on the nose the board still support’s your weight without sinking. Of course, the difficulty is being able to backwind sail. I find this method to be the best for me especially when schlogging a sinker.
But however you do it, you need to practice in light wind and flat, shallow water so you can build muscle memory. Most people only practice tacks after a long reach instead of practicing tacks for 30 minutes in a small area. A little practice in light wind will save you much pain when the wind picks up because you will have the built in muscle memory.