EVERY brush manufacture recommends using Borax as a cleaning product, so no worries using borax. I have used shampoo/conditioner (as well as borax) for round about 4 years on my shaving brushes, and have not had a problem. In fact - I breathe new life into old "scratchy" brushes by working a decent quality hair conditioner into them, and letting them sit (treated with the conditioner) for 20-30 minutes. Makes it SUPER soft, and the hair looks/feels a lot healthier, with a new "restored" shine/look to it.
joel (at) badgerandblade.com