I'm surprised the pro shop wasn't a little more proactive when it came to a customer buying a performance ball, but then again, some shops aren't as good as others.
Hopefully you have a microfiber towel to use to clean your Hot Sauce, if not, that's fine, but these towels do a bang up job of absorbing oil and not spreading it.
Using your cleaner is a good start, just be sure to wipe the ball down after every shot if you can and clean it with the cleaner after every outing. Most basic ball cleaners can't do much good if you allow the lane oils and dirt an opportunity to soak in.