I don’t know what image you are using, so I can’t tell what is in it and what isn’t, but if it says mysqldump is not there, it is not there. If you have mysqldump on the host or any other container, you can connect to the mysql container from there. Or you can install a PHPMyAdmin or a MySQL WorkBench (at least I used that i the past) for dumping. Depending on how much data should be dumped.
But. if you will run the same container on the new machine, you could just copy the data on the volume. But don1t delete it from the odl machine until you confirmed it works on the new machine.