One word for witches and wizards

I would suggest using either Mage or Magus (plural: Mages and Magi respectively). Both of them convey a gender-neutral magic-user, without giving off a sense of being a mere illusionist.

However, the term "mage" has fallen out of use, with wizard and witch being the standard terms for any magic user. The term "mage" is gender neutral.

I'd consider Mage the more neutral option of the two, as Magus has a slight hint of masculinity from Latin.

Your edit includes what would have been my first choice (sorcerer) (but then again sorceress does exist, as mentioned elsewhere).

With all that in mind, I'll suggest conjurer/or:

"a person who conjures  spirits or practices magic; magician"

(Dictionary reference)

The best word for what you're looking for in my opinion is mage, because it has the same root word as magic, it's gender neutral, and it just means magic-user and nothing else. But you're not going to get much mileage out of the word mage outside of a fantasy context.

I would recommend "practitioner". If you want to be specific, you can use the two-word "magical practitioner".

someone who regularly does a particular activity

Even without "magical", it has a usage within certain literary circles. In the popular novel series The Dresden Files, persons who use magic, regardless of the type, are referred to as "practitioners":

Practitioner is a generic term for an individual who can use magic. The word signifies only the presence of magical talent; it has no connotations regarding the individual's power or skill. There are a number of other terms, however, which do have such connotations.

Obviously, this is used within a specific literary world in this case, but the terminology appears even in other articles:

"Magician (paranormal)"

A magician is a practitioner of magic who attains objectives or acquires knowledge using supernatural means.

The Smart Witch: Introduction to Magic:

One thing magical practitioners have in common throughout history and around the world today is curiosity – the quest for knowledge. We are the original inquiring minds who want to know. There is a reason that so many of the first books printed were grimoires – books of magic – on the whole, magical practitioners are great readers.

The major issue as I see it is that the terminology varies depending on the world you're in.

In Harry Potter, for example, witch is the feminine version of wizard... the type of magic they do is pretty much identical.

In other worlds, everyone who practices "wizardry", regardless of gender is a "wizard" and the practice of witchcraft is very different, and everyone who practices it is called a "witch", again, regardless of gender, though most seem to be female. Similarly, a "magician" could be something different entirely.

I believe that "practitioner" or "magical practitioner" is a word that holds none of the connotations of the individual words have.