G.♣.
I have had many, many kidney stones and have been through lithotripsy at least 5 times (I've actually lost count). I have never been given a choice, as the stones have always been too big to pass on their own.
If your doctor is giving you a choice, it makes me think that this stone isn't too big. Is this doctor a urologist? If not, I strongly encourage you to ask for a referral. Urology is a specialty, and they deal with this every day. You really want to talk to a urologist about the pros and cons. My first concern, really, is that a stone that doesn't pass soon will most likely get bigger over time and ultimately force you to have lithotripsy anyway. Like I said, a urologist is the one to advise you.
Just to let you know, lithotripsy is really not that big a deal. The last couple of times I had it, they did use general anesthesia, but I had virtually no pain or discomfort from the actual procedure. My doctor inserts a stent to make it easier for the stone and fragments to pass, and that's kind of a pain (seriously, it's painful), but treatable with meds. He (my doc) likes to leave it in about a week.
Definitely talk to a urologist. You want to make sure you're talking to an expert.