There is no halachic problem with handing an object to your husband in public when you are permitted to each other, even though it will "give away" your status. In fact, at the time of the gemara, everyone knew when a woman was niddah because she wore special clothes during this time. At all other times she was assumed to be tehorah. .

There is an issue of tzniut which applies specifically to mikveh night. Women should not unnecessarily publicize the fact that they are going to mikveh on a particular night.

The guidelines for public interactions between husband and wife are often a matter of custom (minhag) and not law. For example, in some communities married couples do not hold hands in public although the wife is tehorah, in others they do.

The harchakot, of course, apply during niddah both in public and in private.