I think anyone who normally talks to members of the opposite gender will say ‘its mentchlichkeit’ and those that don’t will say ‘its not tzniyus’.
If you are of the former, then do- as at the very least the other will know what you hold.
If you are of the latter, then don’t- as at the very least the other will know what you hold.
Dating does not change your normative status to each other outside the actual dates. So do whatever you would normally do had you not been dating. It will either be appreciated- or your not both onthe same wavelength.