Does trichomoniasis transfer in any other way than intercourse?

No. Trichomoniasis is considered a sexually transmitted infection - it cannot be picked up from toilet seats, shared towels, etc.
Transmission. Trichomoniasis is a sexually transmitted disease from a parasite called trichomonas vaginalis. Most often women become infected by penis to vaginal contact or vaginal to vaginal contact. It reportedly can infect the mouth ; anus but can not survive in those areas. You will not get if from inanimate objects.