Tips for broken tips?

[EyLayo]

I broke a tip off yesterday. Wondering if anybody has any quick tips to save some trial and error. Planning on shaving down the remaining section with an x acto knife to the diameter needed for the tip. Still not certain on how to remove the broken piece fron inside the tip. There isnt any sticking out to try and grab with needle nose. Cant find a drill bit that small in the garage to drill it out with
[signature]