Gun cleaning question

So I had the urge yesterday, swung by a pawn shop and picked up a sweet little Bersa Thunder 380. It was used but in really good shape...the slide shows some wear but nothing a little cleaning wouldnt fix. Well this am, I remembered I have a touchup marker and put a little bit on and looks like it would be fine. After thinking about it, I read up about it and that's actually a lead free paint. So now I need to take that off and reblue. I am thinking I can just do a good hoppe 9 solvent cleaning, then a birchwood casey perma blue. Should do the trick?