Trash Operations while backing up/migrating

I'm deleting old, irrelevant Time Machine backups from an external drive to make space for a new backup. I just purchased a new computer and want to migrate information from my old computer, which still has a ways to go in fully erasing those two old backups, to my new computer. Is there any risk in performing these two data functions at the same time? My guess is that it won't matter since the data I'm deleting is on an external drive while the data I'm migrating is from the internal SSD on the old computer. Not really a techincal issue rather than a question about reading/writing and wanting to avoid performing two tasks at the same time that might corrupt data.