Grooved fingerboard - how hard it is to fix?

[Pete Wood]

Hi all,
probably a common question. Got a nice thick board on my German 3/4 neck. Had a velvet anima snap and are in the process of ordering a new set. Came to my attention that the board is grooved noticably, say 1mm deep. I don't think it's unplayable at all, but it will need some attention at some stage. We have no money at the moment really. I can just afford to replace the strings.

How hard is it to shave the board down? What the method? How much do you shave it down by?

I've build a number of electric basses now. Two fretless and 3 with frets. I figure I might be able to do it. I've got some straight edges and scrapers. What do you all think?