Assuming that your printers are using a DNS name as their SMTP target then yes, Updating that DNS entry to point to your new server will work.
You will need to make sure your new server is setup to accept mail from these printers. (ie. Printers should authenticate to the server, or your server needs to accept anonymous connections.) You should test this before making the DNS change.
Sometimes printers can be set with an IP address as their SMTP target instead of a DNS name. In that case, you will need to update your copiers or somehow provide an SMTP server at that old IP address.
I find it useful to setup a dedicated DNS name for internal SMTP, like smtp.domain.com. And point all my internal SMTP devices to that address. This way it is not tied to a server name and you can make changes as needed.