I would strongly suggest giving the players constructive ideas on how they can participate in the battle without making attack rolls. I fully suspect the player has little idea what creative options he could come up with to be pacifistic and an asset to the party.
In addition, it sounds like he is genuinely fearful for his characters safety. Perhaps talking with the player out of character and letting them know that hiding and not participating is actually putting their character in more danger (as it is one less combatant on the PC side, and therefore if the rest of the party fails due to your character not participating - who do you think the bad guys are going to focus on next.....your character, and you won't have anyone to back you up).
You don't have to deal damage in order to be a valuable asset to an encounter. They are just the most direct ways of contributing. I gave some other suggestions above. Another option is grappling / shoving.
Yes I actually play with a guy who is good at this (granted, he does attack too if it makes sense). He loves to drop hypnotic patterns on groups and let the party gank them one at a time while the rest stand there drooling. He also likes to hide, cast disguise self on himself, sneak into the enemy ranks, try to convince them that there's another attacking party coming, and they should split up to fight the "other party". Very effective, and very fun.