Here is an idea:
{click to find out about the lady that makes them}
I´d wear something like that either if it doesn´t look like a bra (like the one on the photo), or if it does look enough like a bra to be tongue-in-cheek (yes, my purse is a bra, and no, you can´t touch it). I think the middle ground would be dangerous here, when people would be confused whether the purse is meant to look like a bra, or if it is a bra, or what.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuIeA84x5vDFxLc2KSAK4M7sn9ijgTjOmImMlS9MtjXYPaWk3xjoTTX97_hsLd934GuBHt-oF5mJPy2b7yzvs7438s0YKjYMbDG4WWX0ds1A_N33keIEIRlKAUbtxjnCw-JvmkCrRRuYh8/s1600/siggy.png)