I'm typing this from my 2010 iMac.
FireWire and USB 2 are much slower than the internal HDD which is a lot slower than an internal SSD. After OS 10.7, there are sleep issues with both FW and USB on a 2010. So, while you can, no one in their right mind will recommend it.
Yes, it's still "only USB2", but the SSD -- once booted and running -- should actually feel modestly "snappy", even running over USB2.
(Ok, the armchair
"experts" who think an iMac should never be opened because they're afraid to may not agree but they are stupid wrong when it comes to a 2010). Booting from USB 2 does not feel "snappy". I have a USB 2 SSD with El Capitan and can boot my 2010 with it any time I want to be reminded of this.
It's time to invest some money. Since the NV RAM battery is now 8 or more years old, time to replace that as well. Call around, get a quote to replace the battery and install an SSD. Get another quote for labor only. If you're handy with tools, consider doing it yourself (this page is misnamed as Intel Macs don't have PRAM).
https://www.ifixit.com/Guide/iMac+Intel+21.5-Inch+EMC+2389+PRAM+Battery+Replacement/6292
Replacing the HDD is only a few more steps once you're in there. You need the following:
SSD — many brands but the Samsung 860 EVO one is hard to beat @ $128 1TB with a 5 year warranty. If you want 2T or even 4T, now's your chance.
https://www.amazon.com/Samsung-500GB-Internal-MZ-76E500B-AM/dp/B078DPCY3T/ref=sr_1_1?s=electronics&ie=UTF8&qid=1542642416&sr=1-1&keywords=860+evo&th=1
Bracket — not absolutely necessary but makes the job easier and provides better cooling $12
https://www.amazon.com/Fenlink-Inte...r=1-14&keywords=2.5+to+3.5+hard+drive+adapter
Without the bracket, use double-stick foam tape to stick the SSD to the foil lining the back. I use the bracket.
Temp sensor. The Apple HDD has a builtin sensor. The fans will roar 100% unless replaced. OWC makes a $40 wiring harness with a sensor but you don't need it. Fortunately, a 2009–10 can use an optical drive sensor taped onto the case $10.
https://www.amazon.com/Eathtek-Repl...2755&sr=1-2&keywords=2010+imac+optical+sensor
(Yes you can control the fans manually via an app but then you
have to without this sensor and they will roar 100% during startup till the app loads—no thanks!).
NV RAM battery. Apple uses the heat-resistant BR2032 but, once you get that spinning heat pump out of there, a common CR2032 medical battery works perfectly well. Under $4 at any drugstore.