A somewhat unusual suggestion...
Hi TryingItAtHome,
While I agree with the other response about exterior paint in that it will be less likely to fade. May I humbly suggest the somewhat maligned (and forgotten) art of pyrography?
Since it burns/writes into the wood, you know it won't fade, and doesn't really need any additional carving steps. Obviously, you also won't have any paint/brushes to buy. If you have a lot of labels to do, it may actually come out cheaper, easier, (and less messy) than buying paints/brushes/cleaning stuff. Carbatec sells pyrography pens for as little as $80 (probably even cheaper on AliExpress/eBay) and with a little practice, should have little difference from writing with a sharpie.
Anyway, just some food for thought...
Hamish.