^^^ If you're going to do that, probably won't need to remove the bolt anyway.
Plan B: remove the stock & trigger group, with barrel pointed up, hose the receiver with BRAKE KLEEN, blow out with compressed air, squirt in a generous amount of your favorite spray lube, let it sit for 2-3 minutes, blow out the excess with compressed air, re-assemble and enjoy.
This may seem sacrilegious to some but it does work. My guns aren't runway model range toys, they're working tools exposed to dust, weather, and whatever 'stuff' comes along. 10-22's aren't normally 'finicky' when used with HV ammo nor do they require frequent, extensive cleaning. If the ammo being used seems 'dirty', change ammo type/brand. I (and my 10-22's) prefer Federal HVHP for daily general purpose use or Federal Auto-match for practice/range use but in reality, most domestic production 22 rimfire is acceptable for recreational use w/o creating a need for constant cleaning.