Others here will probably be able to advise you better than me, but this is what I would do if I were you:
1) First upgrade this computer to El Capitan and do all the security updates you can on El Capitan. This is so your device can get all the firmware updates that it needs . Take the device as far as it can go on El Capitan. Even on a supported Mac, you cannot go straight from Snow Leopard or Lion to Catalina— you have to make some pitstops in between so your computer gets the necessary firmware updates. In your case, If you are starting on Snow Leopard, You might need to go to Lion or Mountain Lion first and then jump to El Capitan. You can find out information about the “OS jumps” that you can make on Apple‘s website. Firstly, You need to upgrade this device as far as it can go, before using DosDude1’s Catalina. The Dosdude1 demonstration video on YouTube is taking an unsupported Mac from El Capitan to Catalina….
2) make a Catalina install usb stick like dosdude1 advises.
3) if you want to install a dosdude1 Catalina on an external HDD, it may be possible, but it will probably be extremely slow And not so much fun to use. Catalina was designed with SSDs in mind. So if you’d like the computer to be comfortable to use, After you upgrade to El Capitan, and after you’ve made the dosdude1 USB stick, you can install Catalina on an external SSD or Swap the iMac’s internal HDD for an SSD. With an iMac 8,1, an internal SSD would probably yield the best results. You can find a 2.5 inch SATA SSD For that iMac for relatively cheap. while we’re on the topic of the internals, you should max out the ram for this iMac before taking it to Catalina also. Catalina requires at least 4 GB of RAM, your iMac can take up to 6 GB(unofficially), I believe. Maxed out ram and an SSD will give you the best results with dosdude1 Catalina.