putting skin cream in a different cream bottle/container?

For travelling purposes I wanted to get a smaller package of face cream, but it turns out they don't have ones of my preferred everyday face cream at any of the stores I've been to...

So I found this other small cream bottle (also facial) from a different brand and the cream is a couple of years old, but its package is perfect for the amount of the cream I need for my trip. I was wondering if it was hygienic to remove the (a bit old) cream content from the small bottle, maybe rinse it, and put my everyday cream in there? Is it possible that the everyday cream will change its composition in a new bottle and cause damage to my skin?

The old creme is chanel and the new one is avène, they are both for moisturising..