If you are getting a shimmy, and pulling to the left, I would suspect the possibility of more than a simple alignment problem...although that is possible. You are right in assuming that many dealers are ill prepared to handle this. My tech had to call BRP to learn the procedure, then the dealership had to purchase the necessary tools...at the local home improvement store.
Because of your shimmy and pulling, I think you need to do a thorough inspection first. Bad (loose) ball joints, loose fasteners, bad tie-rod ends, or worn shock or a-frame bushings can readily cause both a shimmy and an alignment problem. Loose wheel bearings can do the same. Also check runout for a bent or badly machined rim. You could actually be dealing with multiple problems that are not necessarily related. The dealer also needs to check the steering sensor zero, via BUDS.
While you can do the alignment procedure yourself, but if any adjustments are made, the steering sensors will need to be reset afterward...
by the dealer. The procedure is in the shop manual, and requires an 8' length of aluminum angle, marked at the center and a foot from each end. Two 7" metal straps, four clamps, a tape measure, and a magnetic laser level. The Spyder must have the wheels removed and be jacked up to do the alignment...although I do not believe in this method.
You can do a quick spot check yourself, with two
straight 2x4s. Lay one against the outside of each tire, with the wheels straight. Carefully measure 3' ahead and behind the wheel center. I would suggest flipping the 2x4s over and measuring again, in case the boards are not perfectly straight. Average your measurements. Subtract the front measurement from the rear. A positive difference indicates toe-out, which is bad. A negative number indicates toe-in. The spec calls for a -10 mm toe-in for the RT, but this is with the suspension unloaded. On the ground, you want to be at zero. The RS should be zero, too, but that spec remains zero unloaded (???)
The preferable measurement is with the rider aboard, but it is difficult to measure while sitting in the seat.

I would do this spot check at three different places, rolling the Spyder slightly each time, just to negate any effect of tire sidewall variation. Remember that this is only a means to check...it is not a true alignment. If you find a suspected problem, see your dealer. He can get an education from BRP in the correct procedure.
The need for adjusting the sensors comes from moving the steering components. There are two different steering centers...the handlebars and the wheels. The handlebars could be straight, but adjustment could move the wheels slightly to one side or the other. Basically, you are assuring that the handlebars are centered, the wheels pointed straight ahead, and the steering sensors both synchronized to each other, and zeroed when the steering is set straight. Remember that with DPS, the sensors determine the steering assist. You do not want them trying to steer you, or fighting each other, when you are moving straight ahead.