J1 or J2 visa for post-doc
You should apply for J-1.

I had exactly this question when my wife got accepted for a postdoc in the USA.  She started before me.  I was told that although it may be possible to work on a spousal visa, it is far easier to get J-1 directly.

Note: One difference was that we both got paid.  An unpaid postdoc sounds quite exploitative to me, to be honest.