There are options. There are a few ways that veins can be treated on the leg. If they are smaller than 2 mm (usually known as spider veins) they can be successfully treated with a laser and no injections. If the veins are larger they must be treated with injections to avoid serious complications. I suggest that my patients also seek out a vein specialist that has an ultrasound to look for "feeder" veins.
Usually not. Laser treatment of leg veins is somewhat uncomfortable, but not intolerable. It is common to use ice or some other form of cooling applied to the treated areas, both before and after for comfort; and it works well. In any case the discomfort of the treatment does not last long.
IV not necessary. Laser treatment of spider veins is done only with a topical anesthetic or no anesthetic at all. Laser treatment of varicose veins involves sealing the leaking valves with the laser followed by microincisions to remove the varicose veins. This requires no IV but does require several needle insertions along the veins to numb them. This is called tumescent anesthesia. It is very well tolerated.
It all depends ... On what needs to be treated and how it is to be done. Sometimes, nothing is needed. Sometimes, some local anesthetic in the form of a shot is used. Sometimes, IV sedation is used (but this generally isn't necessary).
Either or & more. It can involve any of the above plus the use of lasers or intense pulsed light or infra red therapy.