RP Cat is correct about the risks of not having the surgery.
There is a method of acupressure that doesn't involve actually inserting anything (I don't recommend using a Q Tip as you may injure her or cause infection.) But the only times I know of people using acupressure to induce ovulation instead of just have a cat de-sexed is if the cat is a pedigreed cat, an excellent example of the breed standard, who has been (or is currently being) shown and titled and is going to be later bred in a breeding program to preserve and improve a breed. If that were the case for your kitty, you could ask your breeding mentor about this.
But even then , breeders may do this a few times now and then in between breedings or to delay a first breeding if she is too young and having frequent cycles, but they get the queen spayed usually before age 6 or 7. They do not use this over and over and over for a cat's entire life putting her into one false pregnancy after another. that increases the risk of cystic endometrial hyperplasia.
http://www.docstoc.com/docs/37336154/Susan-Little-DVM-Diplomate-American-Board-of-Veterinary
Why not get her spayed ? This is a very common surgery. I think it would be best to just get some earplugs and telephone your veterinarian to make plans to get her spayed in the near future after this cycle. If your cat has some medical condition that makes it impossible to put her under anesthesia then you will have to discuss it with the vet. then maybe it is matter of choosing a lesser risk, and you can ask the vet if he knows about the acupressure technique.