I "cheat" at pulling manes all the time - we never go to big enough shows that require braiding.
The method is the same as the "real" way, but instead of pulling out the hair, cut it instead. So, you'd grab the long ends of a section, tease back the rest, and then just cut the pieces you would have pulled (up as close to the neck as you are able). Brush that section back straight, and repeat. It keeps a natural looking edge because the cut hairs are hidden up inside the rest of the mane. I use a mane pulling comb to do the teasing, and a scissors.
I can do a mane in 10 minutes or less this way, and the horses are much happier. It turns out looking just fine - the only watch-out is that for horses with super thin scraggly manes you can sometimes tell where it was cut, so I cut the hairs a lot longer (close to the finished length I want).