First, whatever you decide to do/use, I'd be sure you try it on a part of the floor that is inconspicious. Because, if you don't, and you end up discoloring or damaging the floor, you'll see it ALL the time.
Contact the folks at either PeelAway.com or CitriStrip.com for guidance. I'm not sure if what they offer is OK to use for both Latex and Oil-based paints. (Ask them ...)
Other than that, a somewhat 'dull' razor knife may work if you scrape very, VERY carefully. My best to ya and hope this helps.