Cleaning oil from pewter plugs

The keys on my early 1800’s Goulding/Potter flute do not seat well. I’ve been advised to occasionally add a drop of oil to the pewter plugs (valves?) to help seal them from leaks, and this seems to be doing the trick. The whole flute likely needs a thorough overhaul, but for now I’d like to do some proactive maintenance.

My concern is oil buildup in the brass sleeves where the plugs seat, and the possibility that dust and other foreign materials will clog up the tone holes.

My question is how can I clean gunk from the tone holes without removing the keys themselves? The space is too narrow to allow access to the residue.

Note: I have not actually noticed any significant buildup, but I’d like to address this before it becomes an issue.

Thanks,

Tom