What is the best way to resurface the spray needles so that they work properly? (I don’t have one of those 1” belt sanders…yet.)
lathe works the best. Or put the needle in your drill chuck and carefully file or sand paper it down while its turning.
Just expanding a bit on what Peter recommended, I grap the piece in my lathe chuck by placing the T part behind the jaws. When turning at a good speed, I use a very fine file to get the angle I want. I try to follow the existing slope and try not to get a barrel shape. I finish with very fine sandpaper, say 1000 grit to polish it. They come out really nice.
If you use a hand drill, you need a fork and a guide to hold the needle steady. There are instructions to do that in the MTFCA pub on carburetors. Its not near as good as using a lathe.
There were instructions published once a looonngg time ago in one of the T magazines. Suggestion was to have a machinist take a block of steel, true up two perpendicular sides and bore a guide hole through at the appropriate angle so that the needle could be slipped down the hole and taper could then be parallel to the side of the block where the taper exitted. The steel block should be large enough to support as much of the needle body as possible. You could then hold a file or whatever flat on the side of the block and by rotating with a little pressure on the needle, you could get those pesky grooves out. The block helps steady the needle considerably when using the "fork" and drill method.
I made a block like that using hard maple. It works well using a file, as Warren described. I found that a pegboard hook can be used in a drill to drive the needle using the two holes in the "T" at the top. After filing, I polish the tip on a buffing wheel.