Just be aware that tennis is going to be putting different stress on your feet than running does. When running the emphasis is on pressure, and putting your feet down gently. Most of the stress is just in up/down motion. In tennis, you are cutting a lot and changing directions, which is putting a skew force on your pads. If all you have been doing barefoot is running, they may not be adequately prepared for that.
In my case, I'd done a lot of barefoot hiking before I started playing tennis barefoot, so that may have prepared me better.
Also be aware that running (or hiking) on most surfaces stimulate the sole to build up tissue; tennis, however, tends to sand it off, so I sometimes get into a struggle between enough hiking to add skin and tennis that removes it.