While it's best to use a "real" server, that doesn't mean expensive, and you can at least take steps to make your current setup more secure.
Start by disabling WiFi on the printer. With that disabled and no network cable connected to the thing, the only way into it will be through the computer it is connected to. Having a single entrance to secure is much easier than having 2 or 3.
Next, make sure you've got a decent and up-to-date antivirus package on that computer, and if that computer won't be doing anything besides printing, set the antivirus software to a high level of protection, scanning everything all the time.
Typically, queued print jobs are stored as files in the host computer. The antivirus software should scan files as they are written by default and it should help mitigate the issues you mention in that way.
Also, make sure the operating system is getting its patches and reboots itself automatically outside normal office hours to apply these.
Next, check the permissions on the printer share. If you have a domain, make sure that only "Authenticated Users" or "Domain Users" are allowed to print.
Extra Credit
If you feel up to the challenge, the only thing limiting your current normal desktop from being a "real print server" is the operating system. While something is to be said for working with something you're familiar with, if you really want the most out of your printer as a shared network device, try running a non-Windows server OS, such as a Linux variant or similar. This shouldn't cost any extra in licensing or hardware, though it will cost in your time.
But, set up properly, converting that basic desktop into a real server will give you more control, and importantly, more security, than the basic desktop OS hosting the office printer.