Worthwhile to stop at your local welding supply shop and pick up one of those little pocket sized torch tip cleaning tools. Handy to have in the tool box, lots of selections of very fine wire probes, not expensive. A gotta-have for the weldor, useful for many things.
If a primer (or percussion cap) actually damages the rifle, you have no business shooting the thing anyway. BUT! There are a bunch of things that can plug a small hole. Even a grain of sand, if the hole is small enough. If you have a set of picks, I'd try those first. Harbor Freight has a mini hook and pick set for $1.99, and larger/more expensive set. Try something like that. Or embed a sewing needle in a chunk of dowel, and use that to try to pick the blockage out. HF also has sets of miniature drills. If the pick won't do the job, try a fractional millimeter drill in a pin chuck. Their micro drill bit set is $3.99. They don't seem to have a pin chuck these days. Amazon.com has several. https://www.amazon.com/s?k=pin+chuck&crid=1RKAG4460ZFIO&sprefix=pin+chuck,aps,157&ref=nb_sb_noss_1
Where are you located? Pretty sure I have bits that small
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