Graig Lwyd 1
Image by Kammer

Yes, probably - don't forget to show it to the county Portable Finds Officer (I'm assuming Wales has a similar scheme to the English one) "Neolithic polished axe". I suppose there's an outside chance it was a whetstone for a long-bladed scythe - the museum guys should know the local types best. It'd look best with a proper shaft.

D'ya wanna buy some water-worn axes? I can sell them by weight or colour.
I could send you enough axes to build a rather small wall.

In this months Cumbria magazine, they've got an article on Tony Greenbank, the fella who builds Goldsworthys walls.