0.6 mm or 0.6 cm? I would guess the latter.
6mm stone should still pass (and ultrasound generally shows them larger than they really are as there's estimation of size based on size of kidney, so it's not exact science), alas quite painfully. First thing I would do (and I've been battling stones for past nearly 30 years, and had shockwave done previously), is finding out what kind of stone it is. 2 main types are calcium and uric acid. Mine are the latter, so they are also a hint to other challenges like gout that can follow.
Then depending on the type of stone, take medication to melt them. Pocitrin Tab or Uralit-U (you can get them without prescription in pharmacy opposite Siriraj hospital) would take 3-6 months to melt the uric acid stone your size enough to pass on its own. Obviously if stone is calcium, you would need different medication, but working in the same way - slowly melting it away.
Drinking lots of water also helps as it prevents crystals from forming in kidney, which can then lead to kidney stone formation.
One way to know if your stones are uric or calcium is whether they show on x-ray or not. Calcium will, uric acid will not, or very faint.
As for blowing them up... I wasn't sedated nor had any pain medication administered, but the feeling was like if someone snapped me with a rubber band in the same spot every second for close to an hour. While that in itself was a bit annoying but not really painful, the bleeding from kidney that followed made me rethink whether I'd want to do it again. Yes, it wasn't invasive surgery but it still caused fair bit of damage to kidney itself.
As such, I would recommend going the way of melting it, and letting it pass on its own.
If it starts to pass too early and it is blocking the way, there will be pain. Provided you are not taking any hypertension medication, painkillers can be used to control pain. Buscopan won't do anything, but Nurofen or Tramal would. I have found Nurofen work better than others, and it's easily available over the counter (Nurofen Zavance). However - If you are taking any heart medication or hypertension medication like for instance Valsartan, that will cause kidney failure!
So careful with painkillers. Although if you only take medicine to melt stones, there's no interaction between them.