If it's a DE just turn the head North-South and it'll get in there. Schick injectors are great for the tight spots too though.
I just use a beard trimmer w/ no guard. But, if you're careful, you can get a DE in there with side to side passes. Up and down will probably result in cutting your lip. Ask me how I know.
I do use tweezers but really takes out the manliness feeling I get after shaving with my DE razor haha
+1 (Dovo shavette) Maybe a square point/spike point straight. Then again, the shavette would probably be best.
If I'm going to attempt trimming/cleanup with a DE, I use these first. They are of excellent quality and made specifically for moustache/beard trimming. Don't waste your time with the nickel plated or oxidized coated models, get the 100% stainless. These can be re-sharped when/if necessary, and as long as you don't abuse them they will last a lifetime. I got mine here: https://www.thesuperiorshave.com/dovo_shears.html#43