As a former journalism major (who has used almost none of those skills professionally), let me tell you right now that you DO NOT make changes to what a person says EVER.
Don't misrepresent what the interviewee says. Don't misquote them. Don't change the meaning of what your interviewee says.
But you can leave the word whiskers out. Leaving out all the Ahh..Umm..Err... is just good journalism. Word whiskers rarely (if ever) add anything to the conversation. If you've ever read an interview in a magazine, listened to one on the radio or watched one on TV, it's been edited and most of the word whiskers have ended up on the cutting room floor.
But word whiskers tend not to be a problem if you're interviewing a famous person or someone who speaks professionally. Avoiding word whiskers is Public Speaking 101 kind of stuff. A lesser skilled interviewee will, obviously, not speak as eloquently. So what then?
A quick word on [sic]: [Sic] is not for interviews unless for some silly reason you're doing the interview by email. (Sic or sic erat scriptum literally means thus was it written not thus it was said. Even then [sic](in my own personal experience) is woefully overused.) Since you don't use [sic] in interviews, when people say things in their own personal style, which may or may not be grammatically correct, you quote them verbatim. One exception to this is people who give long, rambling answers (or use an excessive amount of word whiskers). This is when when your frenemy, the ellipsis, comes into play.
(This point is less important in the digital age when stories are no longer measured in terms of column inches but is nevertheless still critical in journalism.)
Proper ellipsis usage is key: Ellipses are okay if you do not change the meaning of what's being said. For example, here is a quote from an interview on gun control given by US Vice President Joe Biden, a man known for long, rambling answers:
It is an individual right, but it is also clear constitutionally that
the government can limit the type of weapon you can own. For example,
if the idea was to be able to repel a tyrannical government, then you
should be able to own an F-15 if you have the money to buy it, with
full ordnance. But you’re not allowed to do that, and the court says
you can deny certain weapons available for individual ownership. You
can’t have a nuclear bomb. So it is an individual right. You have a
right for self-defense against any intruder or any illegal activity
being perpetrated on you, and for your physical self-defense.
BAD Ellipsis use:
It is an individual right ... to own an F-15 if you have the money to buy it ... you’re not allowed to ... deny certain weapons available for individual ownership ... a nuclear bomb ... is an individual right. You have a right for self-defense against any ... illegal activity being perpetrated on you, and for your physical self-defense.
As you can see, Biden's words have been twisted to mean the opposite of what was said. This may be an extreme and obvious case but even small, seemingly innocent omissions can change meaning.
BETTER Ellipsis use:
It is an individual right ... [to] self-defense against any intruder or any illegal activity being perpetrated on you, and for your physical self-defense.
In this case we have distilled VP Biden's words to their core meaning: You have a right to self-defense, period. Also notice the bracketed word (another frenemy). The way Biden's words were summarized would have been grammatically incorrect, so the [to] was added to fix that. Please note: the meaning was not changed, only to correct grammar which would have otherwise been incorrect due to my editing.
One final thought: Be sure to record the interview (with the interviewee's permission, of course). Keeping everything on the record will help you accurately transcribe the interview (and keep you honest while doing so), as well as provide self-defense if the accuracy or intent of the interview is in question.