Many chalazions will disappear of their own accord. The likelihood increases if you use hot compresses every day. But it's entirely reasonable to get fed up with waiting after say 2-3 months & seek referral from your GP.
Some eye departments direct chalazion referrals straight to a minor operations clinic to speed the process up, so it's possible you might be offered the op at your first visit.
Frankly, the local anaesthetic does sting a bit for about 5-10 seconds. After that it should all be painless.
Op takes about 60 seconds, and the lid will be a bit swollen and bruised for a few days afterwards.
You just have to decide whether the chalazion is bothering you enough to be worth 10 seconds of mild stinging.