I liked the look of SEAL last I saw it, and could swear there was a port of the Lynx browser to it, but perhaps not.
If you do need a standalone browser, I think
Arachne is as good as it gets on DOS. Whether you can find appropriate network drivers is another matter.
NewDeal Office is also interesting - based on the old GeoWorks package, itself descended from GEOS - but 1. it was designed to pretend to be an OS, so running it under DOS might be some hassle (I *assume* they built on top of Caldera OpenDOS/DR-DOS or FreeDOS, but no idea)... and 2. the company appears long-since dead.