**It is forbidden for a nazir to cut his hair completely no matter what tool he uses.** The Rambam writes (MT [Nazir 5:11-12][1])

> When a nazirite cuts off one hair, whether using a razor or a scissor,
> he is liable for lashes, provided he cuts it from its roots as a razor
> would. Similarly, if he pulls out [a hair] by hand, he is liable for
> lashes. [...] If he left enough of [the hair] so that it could be bent
> over for its tip to touch its root, he does not receive lashes,
> because [cutting in this manner] is not [equivalent to shaving it]
> with a razor.

(see also [footnote 28][2])

It is theoretically possible to shave without a tool or one's hand but with a cream, see 5:12

> If a person applied a potion that removed hair to his head and in this
> way, removed his hair, he is not liable for lashes. He is, however,
> nullifying the observance of a positive commandment, as [Numbers 6:5]
> states: "He shall let the mane of the hair of his head grow."


  [1]: https://www.chabad.org/library/article_cdo/aid/983589/jewish/Nezirut-Chapter-5.htm
  [2]: https://www.chabad.org/library/article_cdo/aid/983589/jewish/Nezirut-Chapter-5.htm#footnote28a983589