Your concern indicates you can't afford either to show.

Therefore you should just buy yourself a cheap pay as you go, cellular "TRAC" phone.

You can purchase these at a multitude of places starting with cell phone retail stores. A dedicated "hobby phone" and 50+ minutes of usage time should set you back about $100. When you need more usage time you merely purchase a new "time card" for whatever amount you want to add to the phone.

Voila!!!
No itemized bills for your wife/SO or employer to scrutinize and question you over.

Mine shows phone numbers, that's it. By the way, it's still not illegal to simply call an escort service.
The prepaid cell phone is the best bet for those who are married or want to be ultra secure.