EVERYONE has a tremor and I imagine most would have difficulty cannulating an artery in a mouse, assuming they are smaller than those in our NICU babies which we find difficult.
The trick/solution is that you must rest your hand on something while doing the procedure. Having your hand resting in mid-air is a sure-fire set-up for tremor and difficulty in keeping things steady enough to do that fine work. Use your instruments to their maximal effect. If you cannot thread the catheter with your hands, use a set of Jake's or Jeweler's forceps to hold the catheter while you cannulate. An A-line wire will give the catheter enough stiffness to allow for easier cannulation (if you are threading without a wire). If you have access to loupes or a magnifying lamp, that would help visualize the artery better as well.
best of luck...