That's another great question, and one that's been discussed often. Here are some posts to check out about other folks' experiences. And yet one more to check out, about vaccines in general, where I said:

When I was fighting cancer, my pawrents debated whether or not to vaccinate me. While I did get a kennel cough vaccine, we skipped the rest of them. Recently, the AVMA has recommended that dogs with immune-compromised systems get excluded from rabies vaccinations and many holistic-minded vets lean toward not vaccinating a dog with cancer at all. You can read more here:

Rabies Vaccination for Cancer Dogs

Many vets are still following old protocols for vaccines. I personally don't think they are a good idea when you're fighting cancer, only because like you said, the body is already immune-compromised. I'm not a vet so please take that for what it's worth. Instead, I prefer titering (basically measuring the body's immunity to vaccine diseases) to vaccines in this situation. 

When it comes to ticks and heartworm medications, that's a whole other ballgame. Here are two good nutrition blog posts about it. Avoiding fleas, ticks and heartworm without using chemicals is absolutely possible but takes a lot of dedication and commitment to following the direction of a holistic doc, feeding an excellent diet, daily grooming and keeping your home clean. Our pack has so far managed to avoid a flea and tick problem without using chemicals, but we choose to use heartworm meds because of where we spend most of our time, and we're not dealing with cancer in our dog Wyatt Ray .

If you decide not to pursue traditional vaccinations or flea/heartworm medications don't do it on your own. Find an excellent, qualified holistic veterinarian. In your part of the world I know there are quite a few to choose from. Our Resources Page has a directory where you can search for one.