Use the web uploader inside Chrome or Firefox - it has auto-resuming capability so that you can disconnect your Internet connection to pause the upload and then reconnect when you wish to continue the upload.

If you want to avoid losing Internet access from other programs, just change temporarily the browser's network settings to e.g. some non-existent proxy. This will kill connectivity just in the browser.

If you need browser access, either start the uploading in a separate/dedicated browser, or use some browser extension that let's you set proxy settings on a per-tab basis.