There are standalone GPS loggers that lack transmitters and log location to SD cards in CSV / GPX formats (e.g., [0]). It's one more thing to carry, but it's small and you can be reasonably confident that it won't transmit your location to anyone. But the particular one I've posted doesn't have the ability to encrypt the data as its being saved, so if someone physically steals the device, they'll have easy access to your past location history.

[0] https://canadagps.ca/collections/gps-data-logger/products/co...