Surely the colonists brought with them at least some sharpening equipment to maintain axes, knives chisels etc., and I imagine every ship would also have some too.
Maybe sandstone for the coarse work and english slate for the finer. Apparently coticule was known from Roman times...

What I'm wondering is - Did they shave? and if so what would their razor look like and how would they hone it ? Pictures show a mix of beards and clean shaven- I wonder how accurate though. Maybe a historian will know.