Maybe just ...‾ないで?, or are you looking for something more formal?

I'm pretty sure ずに would come across as formal in spoken language. Hmm..listening to the teachers around me, I will also hear (in speeches, whatever) something along the lines of

諦めることなく、

Although that also (I believe) has a bit more punch to it.

Back to the issue, though, I'm pretty sure a ずに followed by an appropriate conjugation at the end of the sentence would be as polite as you need to be. If I remember (my mind is a bit spotty, so I probably won't), I'll ask someone tomorrow.

Just looked it up - they are slightly different.

ずに meanings "without", as in, A ずに B = "doing B without doing A"

Here's an example:

切手を貼らずに手紙を出してしまった。 Shows you not doing something you'd normally do with the following action.

途中であきらめず、最後まで頑張ってください。

Not quite the same - in this case, it is "don't do A, do B"

出発前日まで予約が取れず、心配させられました。

In this case, it shows a tight link between the lack of A and it causing B. In this case, "I didn't/couldn't do A, so B"

These examples, by the way, are from the EXCELLENT 日本語文型辞典. It's made for teachers of Japanese, or high level students. Very, very good explanations (although it's 100% Japanese)

http://www.amazon.co.jp/%E6%97%A5%E6%9C%AC%E8%AA%9...

Hey everybody:-) quick question - I saw in one of the examples for 代わる that this form is used without the に - so, ...いつもと代わらず健康... is this a mistake, a different grammar or maybe an exception? Thank you:-)