This is a good question Franziska, thanks.
For one application I ended up with Lucas Marine calcium sulfonate and it sits in a grease gun in a box all by itself with a half tube extra in the bottom of the box. I cannot remember exactly why, getting close to 20 years ago, but it seemed a good idea at the time...
All the other grease tubes I have are lithium-based and range from stuff I got at the farm store to Valvoline Cerulean, which is for heavy equipment
but not specifically marine. It is also billed as low in heavy metals and allows one to 'consolidate' grease types. This is how I would go forward, pick a medium to high grade lithium grease and just have one type around. Is there room onboard for one 1/2 liter tube and the applicator gun? There are mini guns
too. The gun that has the Cerulean is also labelled.
A moderator on another forum (iboats?) used to sign posts with 'any grease is better than no grease at all' and I think there is wisdom there. If you have something apart to grease it, clean it well and replace the grease with something known good that you can source and refresh next time without much effort.
And if you are so far away that your favorite type is not there, use what you brought or the locals have and tell us a good story about it when you get back