There is nothing illegal about cross dressing or about carrying women's clothing, so there is no problem there. Your question is about avoiding something that would be embarrassing to you.

While there is no way to guarantee anything, there is little likelihood that clothing would set off any questions. When x-ray'ed the TSA does not know whose bag is whose, generally. If they have to open the bag, they ask whose it is, so they would not likely be able to say man's bag or woman's bag as it moves through.

If for some reason they decide to search the bag — likely for reasons such as liquids or something they cannot figure out — they do it over to side (you could ask them to do it if they do not offer) or even privately. This could be embarrassing in its own right, but what is in your bag would be unknown to co-workers.

Bottom line, follow the rules and pack toiletries, electronics, and chargers in your briefcase, and you will likely never have to worry.