For starters, it's perfectly safe to wax the scrotum if the correct technique is used.
The general consensus is that hot wax is far preferable for intimate waxing than strip wax - and the most respected male waxing trainers in the country (Kim Lawless -
The Wax Queen and Andy Rouillard -
Male Waxing Training) both teach male intimate waxing using hot wax, as does Lori Nestore (the US Wax Queen). Generally, hot wax will give you a much more comfortable intimate waxing experience as well as causing a lot less trauma to the skin.
Obviously, hygiene standards should be particularly impeccable for any form of intimate waxing; you should expect the skin to be pre-cleaned at the start of the treatment (some therapists will provide you with a "wet wipe" so you can clean the area yourself if you prefer), it's also normal for the therapist to wear gloves, and strict hygiene procedures should be adhered to (e.g. no "double-dipping" of spatulas).
In order to get the skin suitably taut for waxing (particularly the scrotum), your therapist may ask you to hold your scrotum or penis with your fingers, e.g. pulling your penis to one side or the other so they can wax the appropriate area.
In answer to the insurance question, that would depend on things like whether the training course in male waxing that your therapist took is accredited - I know that Andy Rouillard's courses are HABIA accredited, for example. I certainly wouldn't risk getting an intimate wax off a therapist who hadn't received the appropriate training though!