1. yes, you can get 26" cross tyres that go pretty narrow...like 1.75 - 1.9.
2. if you have bar-ends, take them off because they are illegal in cross.
3. practice your dismounts and remounts, and practice shouldering and running with your bike.
4. what kind of pedals do you have? clipless are the way to go.
5. since you most likely have a triple, you might think about adjusting your f.der. to "lock out" the little ring. you wont need it.
6. pre-ride the course and run the lowest tire pressure you can get away with without pinch flatting.
7. depending on your brake setup, you might consider reversing them so that front is on the right, rear on the left....this is to make dismounting easier (so you dont pop the bike up when braking right before you dismount).
8. take off any water bottle cages or other crap thats attached to your bike. you wont be drinking water, and that stuff will get in the way of shouldering.
9. you wont look like an idiot...most cx racers started out doing their first races on mtb's. just go out there and have fun. and prepare to get completely schooled, but dont worry about it...you will learn a ton in the process. good luck!