You have to find the happy medium between waiting too long and not waiting long enough. Very hard to do. As long as the sutures have been removed (the skin is healed up and no openings are present) you can put your hand in cold water, before that, you can use a baggie with ice in it, so if you go ride and it starts to hurt, then ice it 20 minutes MAXIMUM with a baggie of ice and keep your hand dry. It will just help to reduce the swelling. No aspirin as that promotes bleeding. They probably set you up on light stretching, so do that first (pain free!!!) and then do the ice. Remember extra padding on the bars for the time being. As for the new toy, you might as well wait until you're 100% so you can hammer and not do something stupid.
Big thing, you have to remember the 90% rule. When all the swelling is gone, range of motion is back to normal, and you are pain free, you will only be at 90%, so make sure you keep up on your rehab to strengthen the tissues and get to 100%+ so you don't re-irritate the area.
You'll get there, just don't push it or back off. Find the happy medium.