Deoxit is fine and easily available in the USA. Note that they sell many products and often change the names. The common contact cleaner version is Deoxit D5, 5% "active" ingredient with the rest basically naptha, which slowly evaporates. You can also get 100% D5. These come in all manner of containers including spray cans, needle bottles, marker pens. I usually get the D5 spray can with extension tube to flush out some controls, but for finer work I can spray a tiny bit onto a Q-tip or rag for cleaning connector pins. The dental brush sounds like a good idea for the connector holes; for decades I've just put some D5 on the pins with a Q-tip and then inserted then into the other connector.
Caig also sells a contact enhancer for gold contacts and a special lube for faders/potentiometers. I am not associated with them, just a user.