The P1S thread has been done to death many times elsewhere.
You can only log P1S if you are taking a flight test with an Examiner. As an hour builder, if you fill your log book with a load of dodgy P1S entries, you'll have trouble in the future.
If you choose to take an instructor with you in these circumstances, you're not paying him for tuition, you're effectively paying him to be a safety pilot. I would expect that you log P1, he logs nothing and you make him happy by giving him money.
If however during the flight he takes control or delivers instruction, then the logging arrangement may change. You need to have this agreed before you commence the flight.