Safety razors are a no-go with TSA. They might not notice because they're so small, but I wouldn't want to get caught with one.

My travel solution is gillete sensor excel two-blade cartridge razors, with any sensitive skin shave gel. Old school but you can still get them.

Two blades is best for cartridges. More than that will just irritate your skin with no added benefit. One blade lasts for a four-day; it helps to dry the blades when finished.