Mongodump without mongodb
mongo-tools
since Ubuntu 18.04: https://launchpad.net/ubuntu/bionic/+package/mongo-tools
sudo apt install mongo-tools
Ubuntu has the tools separate: mongodb-org-tools
Alpine also has an edge/community package: mongodb-tools
I am using the node:alpine Docker to run mongodump/restore and upload to S3, it works well.
You could also try installing and then copying the binaries, but I imagine they have a lot of dependencies so you might as well find a way to use the tools package, or you'll be creating your own.