Put some English on it?

I've had an idea for a short, dark comedy skit (spoken word). (Given that it's one of my ideas, it has maybe a 3% chance of coming to fruition.) The characters in it are unavoidably British.

I just read this post (thanks to a link by akiko) regarding the outrageous state of American depictions of Russia in fiction (due to a combination of cultural misconceptions and complete ignorance). And it inspired me to wonder whether my pathetic attempts to adopt an English accent* and incorporate some cliche'd expressions ("Jolly good!") would in fact be offensive to Brits. (Note that I don't care whether the intentionally dark aspects of the skit offend over-sensitive folks, who probably wouldn't ever hear it anyway. I just don't want to be one of those totally culturally insensitive jackasses, otherwise known as Americans.)

* My "British accent" is good enough to be taken as such by Americans, but not good enough to even be identifiable as anything at all by an actual Brit.

So, I suppose I have several options, were I to produce the skit:

1. Do it with my "British accent" anyway. Would this be offensive?

2. Do it in my normal American accent. It won't be as funny to Americans this way. And I have no idea what the effect on either humor or offense would be, for Brits.

3. Try to get some people over in England to record lines for me. That's a fair amount of extra effort, especially since this wouldn't be earning money with which to pay them.

4. Spend a lot of effort to improve my fake British accent (and local vocabulary).

So, people who are clueful, would you care to clue me in a bit? (Or refer a clueful friend to this post?)

(Hmm. It just occurs to me that I never made such an inquiry regarding my supposedly country song, "Get Your Hand Out Of My Armpit". But then, I doubt that something that silly could give offense.)

Oh, and while I'm posting, cluegirl has asked folks to pimp out this post asking readers what they want from writers.