Triton X-100 or Tween-20 might work just as well. All are nonionic detergents. Make sure to use a high-quality supply that has not had a chance to oxidize. I recommend these detergent products, which are supplied in an inert atmosphere.
Brij-35 is an industrial polyoxyethylene detergent, that is, purity and length of the ethylene oxyde chain are poorly defined. It is used as a cheap replacement for C12E23. Like all detergents of this class it can form ether peroxydes, which can inactivate proteins. Although removal of peroxydes is possible, it is laborious and involves nasty solvents. Better to buy peroxyde-free qualities to begin with, which are supplied under inert gas. Store in a cold, dark place protected from air.