First to remember is not to try and do deep holes all in one go, do it in stages, and if you have big gaps between the stones infill with smaller ones, take your time, and don't mix too much mortar in one go,
I would use brown sand and put some plasticiser in with the mix as well, once you have got it to the required stage and just before the mortar has gone off gently go over it with a soft dry paintbrush to smooth out the pointing this should enable it to look as if it had been done for years, if doing near a fireplace might be as well to mix a little bit of lime in with the mix. good luck with it,
But if you want a real brilliant finish get a stonemason to do it for you especially as you have gone to the expense of sandblasting it all, be a shame to spoil the look of it, not that I am saying you would. :-) maybe some others on here have better suggestions for pointing.