I can't say for certain, but recently I needed to set new glass into a stone mullioned window. I made up a 3:1 mix of silver sand (labeled as block paving sand at Wickes) and lime putty. Made it a lot easier to get a good finish, has bonded well to the limestone masonry and so far has proved stable.
On one occasion I also made up a mortar using building sand rather than sharp sand (all I had to hand), and used it point in a wooden window frame with quite satisfactory results. The usual sharp sand lime mortar mix can be tricky with closely-jointed masonry, so I wouldn't be afraid of trying alternatives for difficult locations. Unlike portland cement, lime mortar can easily be knocked off if there's a need to change it.