The problem is that not many archaeologists have ever used an axe - much less actually sharpened one - so none of them have much of a clue. The grooves are decoration, clearly.
But, more to the point, I have found some Rock Art in remote Northumberland that I thought you and Fitz might consider evaluating. I am out of the field now - since last Wednesday - and only had time for a one day survey of the cairns and mounds and curricks of Knarsdale. On top of one of these I found a couple of carved rocks, one has cups and channels (quite eroded), another has what-seems-to-be seven of those axehead type carvings on top. I've no photographs of either stone but some of the cairn they sit on are in the pipeline. The Long Cairn is 30m. x 100m., under Right To Roam and with an unusually sympathetic farm owner. It's two miles from the tarmac road but there are sights beside the track to and from it. The cairn might have a blocked entrance somewhere and there is a similar Long Cairn a mile away with similar dimensions that could also have a lost entrance.