Yep, I think the singular is ok, as it could be just one. Seems like it could be both.

Cambridge says...

> In formal styles, we use none of with a singular verb when it is the subject. However, in informal speaking, people often use plural verbs...

Collins says:

> Since none has the meanings “not one” and “not any,” some insist that it always be treated as a singular and be followed by a singular verb: The rescue party searched for survivors, but none was found. However, none has been used with both singular and plural verbs since the 9th century. When the sense is “not any persons or things” (as in the example above), the plural is more common: … none were found. Only when none is clearly intended to mean “not one” or “not any” is it followed by a singular verb: Of all my articles, none has received more acclaim than my latest one.