How to handle disagreement between collaborators on licensing academic code?
If that other 1% of the code isn't anything special (which I'll assume is the case since your question would have otherwise made a point of it), tell the other coder that if he is going to be adamant about it, it will force you guys to rewrite the code, and he might not get any credit at all.  See how he "likes them apples". 

Otherwise, you might search for his reasons (is he hoping to commercialize it?) and find a license that he's amenable to.  There are many licenses that support a basic idea of "open source".

I'd opine that you can't legally use his work without his consent, but you can rewrite it.  But if he made new IP (that is new thoughts/techniques that no one has coded before) encoded in that 1%, you will probably have to negotiate those rights. 

Note that this opinion, is applicable within the academic community where a "shared intellectual commons" has been fairly active for centuries.  It may not be appropriate policy for commercial entities.