Let me add a bit of precision here, because the practical answer and the lease answer are different. The city rule is usually Local Law 57, which applies to multiple dwellings where a child under 10 lives in the unit; if a landlord gets a notice or annual self-audit, they often put guards in every unit to avoid keeping a list of which units have kids. But if your apartment has no child under 10, you are generally allowed to remove them. I would still send a short email to management: 'Confirming that my unit has no child under 10 and I’m storing the window guards in the front closet; please note I will reinstall them at move-out if requested.' That gives you a paper trail.
For the AC problem, the hinged or swing-away models you mentioned do exist, but many landlords use the fixed two-bar kind because they’re cheaper. I had a similar situation in a prewar in Astoria. My solution was to leave the guard in place and install the AC on a small bracket above the bottom bar. I used two L-brackets screwed into the window frame sides, not into the sill, and put a dense foam strip between the AC and the guard so there was no metal-on-metal rattle. That worked for two summers. But do not try to bend the bars open or cut them; that can get you written up for damage, and it weakens the guard.
Also, check whether your window is on a fire escape route; you can’t block that with an AC anyway if it’s the secondary egress. One caveat: if you remove the guards completely, label the screws and tape them to the guard with painter’s tape, because the exact screws for old frames are annoyingly hard to replace.
