What I found helped me most when doing pantos was NOT to stand directly behind the machine with one hand on each handle. Instead, I stood off to the left and held the left handle with both hands. (This is assuming you are working from right to left when standing at the back of the machine.)
Tuck your elbows into your sides and don't move your arms, but sway your whole body. Look ahead to where you are going next instead of directly at the laser. Don't worry about staying exactly on the line, but use the line as a general guide to get from one point to the next.
No one will ever know if you strayed from the line, if you can keep your motions smooth and even. Aim for points if the pattern has them, and hesitate just a tiny bit (not too long or you'll make a knot) before switching direction to get a nice sharp point.
And if all else fails and you are still kind of tense, have an adult beverage first - that should loosen you up a bit!! LOL :-)