Why not buy one decent pen “shell” and then just buy the plastic tube with the tip and the ink afterwards?
I know many companies use pens for marketing but still, they could apply this too and also stand up for the environment while still do marketing.
There are a large number of water-resistant and water-proof inks; both Sailor and Montblanc make several. Legal documents are (usually) required to be signed in waterproof blue or black ink, so you’ll find a lot of selection in especially these brands that cater to business people.
Any ink that is indelible is going to be impossible to get out of clothing if you spill it; I think that’s rather self-evident?