Does this translate correctly?
First, let me go to the washroom.
まず、おてあらいにいきたいんです。
It is literary translated as "まず、お手洗いに行かせて(ください)" and "まず、お手洗いにいきたいんです" is translated as "First, I want to go to the washroom". However it is probably understood as "まず、お手洗いに行かせて(ください)" when you said to someone.
If you want to make clear the demand, you can say "まず、お手洗いに行きたいんですけど、いいですか?".