To expand on iwire's comment: A class II power supply (UL 1310), or a Limited Power Source (ANSI/UL 60950-1), will ensure the output is limited so as to not create a shock or energy hazard.
The INDOOR (dry) voltage limit for what is considered safe for any user to handle bare-handed per IEC/ANSI/UL 60950-1 or UL 1310 is 42.4 Vp (30Vrms) or 60 Vdc. You have that covered. However, you have not indicated anything to suggest the transformer has adequate isolation from the primary to secondary. In order to be considered safe to handle bare-handed, the output needs to be classified SELV (Safety Extra Low Voltage) to ensure it is safe under a single-fault condition. The SELV designation means there will be double or reinforced insulation between the primary and secondary. Alternatively, it is possible to have only Basic insulation with a grounded secondary IF it can be shown that a fault across the Basic insulation from primary to secondary does not cause the secondary to exceed SELV limits. This is doubtful with only one leg of the secondary grounded and no other protection. There are applications for low voltage transformers that do not meet SELV requirements (these would be ELV and not SELV), so you need to be sure you are not using one of these. Just being "Listed", given no other information, does not mean anything toward this end.
The other issue is does this bare wiring present an "energy hazard" that could, for example, weld a piece of jewelry or a tool an operator may be holding, and cause burns. 100 VA is the limit for UL 1310 or a UL 60950-1 Limited Power Source transformer. Routing the non-grounded output of the transformer through the relay contact prior to where the output is exposed to the operator probably satisfies this, but a Listed 5A fuse on the output guarantees compliance with Class 2 / LPS limits.
Any NRTL Listed UL 1310 wall-wart type class 2 device should meet all requirements. Its just when you start looking at bare transformers that safety starts looking like more of an issue.
