Yes you can send perfume and cologne through the USPS mail.
When you send perfume or cologne through the mail make sure to wrap it in some bubble wrap and put some tape around the bubble wrap and perfume bottle.
This will help prevent potential breakage and it's how I've sent perfume before through the USPS without any issues.
Then place the bubble wrapped perfume bottle into another box with some cushioning around it as well.
You just don't want the perfume bottle breaking and spilling in the package while it's being sent through the sorting facilities.