Can I remove and reinstall the hammer in an original 1886 by removing just the hammer pivot screw?

OR

Do I have to do the whole disassembly?

Winchester 1886, I suppose? The mainspring hooks onto the hammer so you will need to pull the stock to access the mainspring hooks. The mainspring tension and retaining screws can be accessed from outside but you really need to have the stock to unhook and rehook the forks. After that, the hammer should lift out. (Honestly , it’s been a few years since I’ve had an 86 apart. ).

This is a Miroku but still an interesting video