Edges around headstock from new finish

Hi. I have a guitar newly finished, headstock as well. The edges of the new paint and finish on headstock are not smooth. There is a slight sharp edge around the top of the headstock from the new finish.

I was going to sand with 1000 or 2000 grit to smooth it out along edge of the headstock, parallel to the new finish. Is this the way to go? Just don't want to chip any of the paint/finish along the sides. Any tips would be appreciated. Thanks in advance,
Pete

Be careful cause the finish on the edges is very thin.

This is very common problem for me when I make painted headstock. I very sand the edges with 2000 grit.

Thanks guys. Do you just go along the edges of the headstock? Or up and down?

Just the edges.