Hillel's Mitzvah to Bathe

Hillel declared that he was on his way to perform a Mitzvah. And subsequntly we learn that that Mitzvah was to bathe

No one questions Hillel's intention to maintain proper hygiene as a valid Torah Value. Yet
what seems "odd" is that Hillel's proof text is a Qal VoChomer from how Romans grace their idols. It seems strange to me that we would learn Torah values, and especially legislate behaviour, based upon non-Jewish norms.

After all, the Hanukkah Rebellion was a revolt against assimilating Hellenistic ideals. It would seem that - even if Hillel's practice is 100% valid - that his "drashah" is quite radical

What say you readers?

Shalom
RRW