Most would say no regarding the two beardies together. Regardless of tank size, the damage they could inflict on one another is severe, and it only takes a split second.
As for the stick, soak it in a 10% bleach solution for an hour, then soak it in pure water overnight (to rinse out the bleach). You could also soak it any favored disinfectant for the prescribed time...so just use what you have. The important thing is to RINSE!
If you have a pot big enough, boiling is also an option.