If you cannot arrange to run a proxy server (definitely the recommended approach), read on:
For information on using NCSA Mosaic from behind a firewall, please read the following. In general, browsers can be made useful behind firewalls through the use of a package called "SOCKS"; the source must be modified slightly and rebuilt to accommodate this. Whenever possible, work with your network administrators to solve the problem, not against them.
An excerpt from the NCSA Mosaic FAQ:
NCSA Mosaic requires a direct internet connection to work, but some folks have put together a package that works behind firewalls. This is completely unsupported by NCSA, but here is the latest announcement:
November 15, 1993: C&C Software Technology Center (CSTC) of NEC Systems Lab has made available a version of SOCKS, a package for running Internet clients from behind firewalls without breaching security requirements, that includes a suitably modified version of Mosaic for X 2.0. Beware: such a version is not supported by NCSA; we can't help with questions or problems arising from the modifications made by others. But, we encourage you to check it out if it's interesting to you. Questions and problem notifications can be sent to Ying-Da Lee (ylee@syl.dl.nec.com).