That would be very difficult to do in my opinion. I am not saying it is not possible at the current state, but I don’t think it is worth a try.
I think a better alternative is to use the search on the actual shop page, that already has a pagination. We just recently added a feature to filters archive pages, including the WooCommerce shop page. There might be a few bugs here and there, but it should be much easier to manage. It is very easy to enable, you can find the related documentation here.