Prepping for Atmosphere

I have one player who loves maps and mapping any and all dungeons and buildings the party enter. There is nothing inherently wrong with the party mapping. In fact the character has bought copper plates and a stylus exactly for mapping their route.

My issue is that mapping the parties progress kills the atmosphere in  the game. It can become almost mechanical, the party enters an area, everything stops while the player updates the map, play continues, rinse and repeat.