A small air compressor such as used by painters and hospitals could be used to fill an automobile tire tube as a supply of compressed air for cleanibg with hose attached. If one tube is used while a second is being filled, you might be able to get a continuous supply of high pressure air at small cost. This is obviously a clumsy system but it might be a bit neater if some kind of low cost pressure cylinder could be substituted for the tire tubes.

will need to be small and always ready

The problem resolves itself into a couple of components. You need a source of high pressure gas. No small hand held blower unit, as far as I know, can generate a stream of gas of sufficient pressure to dislodge loose surface elements for proper cleaning. High pressure liquid hoses now on the market might work but then you must dispose of all that liquid. So you must use an outside source for the gas. This can be either a high pressure cylinder of CO2 or something similar with a hose and trigger valve unit which can be hand held and get into tight places or a small compressor and tank unit which runs on standard electric outlets and attaches to the hose and trigger valve unit. Another alternate is a source of high pressure steam which requires a high pressure boiler unit and probably would generate some moisture as well.

Another possibility would be an ultra sound projector but I am unfamiliar with what is available in a small hand held unit.

The stream of air need not be continuous to be effective. (I also doubt that dynamics would limit the amount of air permitted through a small tube.) The very device within an air compressor used to fill the tank could be used. It works by producing small amounts of high pressure, enough to pass through the tank valve to mix with the lesser pressurized air for later use.

If you want to start from scratch, I'd consider something with a fan intake which leads to a small chamber. At the end of the chamber is a small elastic valve to vent the internal pressure (this would happen many times a second). Add a short straw and it's finished.

You could try this with 120mm computer case fans, which usually work with a 12 volt supply. Most fan makers state how much flow the fan produces—obviously the higher the better. Should the case fan prove weak, I'm sure there are other small-scale fans which will do the duty, like from a hair dryer or a leaf blower.

You could also browse around for small vacuum cleaners (for computers or copiers) which have blower capability (by reversing the fan).