Converting to single chainring
 

I have a double compact 110 34/50T setup right now. I'm looking at removing the larger chainring but I'm not sure if I can use the small chain ring on its own. I can't seem to find any single speed chain rings with 110mm BCD. Is it a very bad idea to just use the old small chain ring?

If you are talking about either SS or FG, lots of people do this. The only issue is ensuring a reasonably straight chain line. You can achieve that with spacers, either on the chain ring or the sprocket. If you are keeping a rear derailleur, you'll have to finagle the chain ring so the chain is reasonably lined up with the middle sprocket on your FW or cassette.

Pick your favorite online supplier (Universal, Niagara, etc). Search for: Single speed chainring, 110 BCD. There are lots. Surly makes them in stainless steel and they are excellent and sold by many online suppliers, such as the aforementioned ones. You can also order Surly rings through your local shop.

If you are talking about single spd setup, main problem, as mentioned is good chain line. The more angled the chain line is to the CW or rear cog, the more likely you are
to derail the chain. If you are talking about single chain ring and functioning RD/cassette, you have the same problem which can be partly ameliorated by retaining the
FD and using its cage to reduce the risk of derailing the chain from the CW. Bolt on outer chainring guards and inside chain keepers can also be used for the same result.
No reason you can't use the original 34t compact CW if you keep these parameters in mind.