如果你不介意 : appropriate translation from English?
I've spent some time in both Taiwan and the Mainland. From my experience, I've heard:

在乎 zai4 hu
在意 zai4 yi4
管 guan3 - More Mainland style... "我不管!"
无所谓 wu2 suo3 wei4 - A really popular phrase to show that you don't really care/mind
随便 sui3 bian4 - kind of like "eh, whatever... I don't care".. Also quite popular


But I've also heard 介意

And if you're looking for that native, colloquial flavor, you can throw in 的话 at the end of 如果, which is just an extension of "if".

如果你不在乎的话,我要去做什么什么...

And what do you mean by "Is there a more common way to prefix such a question?"?