Castor was likable, Syrinx just genuinely was appreciative of him- so when he took her elbow lightly to lead her away- Syrinx did not freak, if anything she turned her face to beam at him. Yes, it was fine to guide her like that. Part of her trust was due to the fact she knew no one was going to do anything while Apollo was around. Syrinx doubted Apollo would let Castor put more than a hand or two on her.
Syrinx wrapped her fingers around the sleeve of his shirt, a sign of 'hey!' and 'I'm listening' in one, tugging a little now and again to communicate thoughts. She tugged twice to indicate that she also approved of this place. It was nice, even if not where Syrinx would pick to hang out.