First off, I wouldn't go anywhere in Raccoon City without a gun. Axes are not good enough, have to get too close and blunt force trauma will cause blood spatter that could get in your eyes, mouth, open wounds. Melee weapons have their place when you have a single isolated zombie and you don't want to give away your position.
Now, having said that.... If I see a group of zombies and a licker, I am going the other way, hopefully unnoticed.... If detected, well, thank God I have the gun lol. Jumping into a fight you can avoid is a needless risk in my opinion. If backtracking wasn't an option then I would try and make myself as undetectable as possible and wait for the licker and group to move along before advancing.