Yeah man, if in real doubt move them to a USB if it makes you feel better and then you should be good to go.
When you boot you select a boot device, in this case your SSD, the partition table tells it where the partitions are and it uses the boot files it finds on this disk.
Those are the old boot files for your old pc. To my knowledge most bootmgr files are similar anyway.
Edit: Add dont remove the pagefile or hibernation file, those are removed if you turn those features off, which you can use your google-fu to solve . Remove the bootfile in the root of your old HDD and you should be able to put a system image on it