Dropbox requires Internet access, while ES File Explorer requires just a LAN (local network).
You can connect your eDGe to Ethernet via
http://www.entourageedge.com/accesso...t-adapter.html (note that only specific models work, and
other users have indicated that if the adapter has the model number "USB2106S", it's compatible).
An easier way than the SD card to share files is a USB memory key. If on your eDGe you're not modifying files, you can probably pull it out without dismounting it first.