Sorry, I only just got around to reading this now, otherwise I would have commented sooner.
For several years, until I went away to college, one of my jobs on the farm as a boy was to muck out (clean up) the dog kennels (we typically might have about 20 dogs at any given time) and the cattery (we typically might have about 15 cats at any given time), I also had to exercise, feed and groom them (where grooming was necessary) and check for transmittable diseases and parasites e.g., including ear canker, lice, mites, fleas, worms in their stool, etc.) and treat them accordingly.
The tools you might use for grooming don't need to be sterilised in an autoclave (as used for sterilising surgical instruments) - that is, boiling water or steam. That really would seem to be "going over the top".
My childhood research on entomology (the branch of zoology concerned with the study of insects, in which I have always been interested) indicated that very hot tap water - about 60°C - will do the trick, as insects and their eggs (including insects that are arthropods - i.e., having an articulated exoskeleton) cannot sustain life after being exposed for about a minute at that temp. You can scientifically prove this simply by immersing insects in the very hot water for a timed period and observing what happens - and this is repeatable.
By grooming your cat's ears, you will be collecting the mites (and anything else) from the cat's fur, onto the grooming instrument. So it is the mites that are in the ears that are the root cause, and this should be treated at the same time as you immerse the grooming instrument in very hot water to clean it. The primary vector (the thing that transmits) for the mites is another cat, not the grooming instrument - the latter being something that effectively just compounds the infestation already on the cat. Your cat will have contracted mites from another cat, and so will be likely to be re-exposed to mites/fleas etc. in its normal social activity with other cats, or off its bedding, etc.
The best approach is thus to treat the cat's fur, ears and bedding with an insecticide that kills fleas/mites - and one that comes to mind that I successfully used on dogs and cats as kennel-boy was derris powder - also freely available for use as an insecticide on food and other plants. It was very effective and relatively harmless - e.g., not as toxic as some of the insecticides animals are treated with today, and which can really knock their livers for six, leading to a premature death (liver failure or liver cancer).
The thing is that derris dust tend to be not promoted/marketed for this purpose today, because it is dirt cheap and the pharmaceutical companies don't have a patent on it for which they can charge a high price. The other stuff they do have a patent on is the only stuff they will offer. Vets seem to be in on this game as well, and only sell the expensive stuff. I have even heard some claim absurdly that derris dust is "highly toxic" to put customers off the idea and buy the expensive stuff which is highly toxic.
So, love your pets and don't treat them with stuff that potentially shortens their life expectancy.