Is there any sign of anything on it? If kshansen's suggestion sounds too complicated, you could simplify it by just going to the hardware store or home depot and buying some threaded adapters that go from whatever size the spark plug thread is [like 14mm or 7/8 - 18, take your old one with you to the store] to whatever size your grease gun threads are. [take it, too] If you tell the guy at the store what you need on each end, they can figure out which ones you need. Then you just need to pump some oil through your grease gun. It isn't hard or complicated, it's basic and might just work. I'd give it a try if it was me.
To determine which plug hole to pump the oil in, you need to figure out which cylinder has it's valves closed. To do it without pulling the valve cover, you could get some different adapters that will connect the same spark plug adapter to a tire type air valve like they use to blow out water lines, etc. Again, just ask the guy, that's what he's there for. That will allow you to use air pressure to determine which cylinder has it's valves closed so you will be able to build up pressure in it. If one of the intake or exhaust valves are open, the air will escape - either through the muffler or carb but if it's valves are closed, it should hold air pressure - at least temporarily - and that's the one to put the oil to.
You also might be able to adapt one of those portable hydraulic hand pumps in place of a grease gun.
I'd also pull that drain plug out and leave a drain pan under it to catch whatever drains through. You can put some fresh oil in if and when it breaks loose.