One of the available options is to use your mobile phone for uploading videos on YouTube - just create a mobile profile on YouTube from a computer outside the organization's firewall and then email the video to YouTube as an MMS message.
Related: How to Access Blocked Websites
The second more versatile option is the one-to-many Hey!Spread - this is an online service to help you upload a video clip to multiple video sharing websites in one go.
You upload the video to Hey!Spread servers and they in turn upload it to the various other video sites including YouTube, MySpace, PhotoBucket, MetaCafe, Google, Yahoo! video, DailyMotion, etc.
Chances are high that access to Hey!Spread is open in your company - they'll send you an email confirmation as soon as your video is uploaded successfully to the different sites.