First, are you sure it's too late to register Baxter? Are his parents registered? If so, your breeder should be willing to help you get him registered, especially if you intend to trial him... It's a feather in their cap if he does well.
If you truly CAN'T register him, all is not lost. AKC now allows non-AKC dogs to enter all performance sports. But you'd have to enter him as "All American" rather than as a Havanese. Also, it is up to the organization that is holding the event to decide whether they will allow non-AKC dogs. In this area, it's a little less than 50/50 in terms of how many clubs are allowing non-AKC dogs. Besides AKC, though, there several other great venues for each of these sports.
For Rally, there's APDT (my personal favorite), UKC, and in some areas, C-Wags. For Agility, there is CPE, TDAA (limited to small dogs), NADAC, USDAA, ASCA and probably others I'm forgetting. For formal obedience, there's UKC and CDSP. So even with an unregistered dog, you'll never be at a loss for things to do.