The contractual cancel threshold is september 30 to cancel per december 31. You get an additional cancel threshold (november 30) if the premium changes, but there's no need at all to wait for that to happen. And if your premium happens to not change you're unlikely to know before the end of september.
If you cancel now you have the following options open until after Xmas 2015, you can act any time between now and then:
a) sign a new contract with a different insurer (make sure it doesn't start too early)
b) change deductibles
c) resolve to not act, meaning you leave the contract unchanged thru 2016
By cancelling now you lose nothing, but gain options a and b. So if you even remotely consider switching insurers you want to cancel now. Some insurers refuse to let you go if you have premiums outstanding, so make sure you have paid all dues by december 31, perhaps make the new contract conditional upon the old insurer letting you go. As there's ample time yet there's no need to use registered mail as long as you get some kind of written confirmation. However, in case of problems you may want to send a 2nd one around middle of september, registered at that time.
You can download a cancel form here
is useless if you need a complete(!) overview of the insurers available in your Gemeinde, in which case www.priminfo.ch
(official federal information site, also features a cancel form, not available in english) is your go-to site.
Some insureres give a small rebate if you pay in advance lump sums. For instance KPT gives 0,5% rebate if you make 6-months payments, and 1% case of one 12month payment. I think similar applies to most other insurers, ask them.
This post is exclusively on mandatory health insurance. If you have additional health insurances, e.g. teeth insurance, make sure you are Ok with the consequences, if any, of cancelling. If in doubt, ask your current insurer before you send the cancellation.