Do I need an in this sentence?

It's fine as written. I would probably have used "since" instead of "as".

You may use the 'as' as written. If you don't want it, you might try two sentences, like "I will sign the form when I start on Monday the fifth of November, 2014. It needs your signature as well as mine.

Personally, I prefer the original use of 'as' as it explains the reasoning for signing when you will do it.

I would work on the thread title.

Or,
I will sign the form when I start on Monday 5th November 2014, as it needs both (of) our signatures .