You can access it as user as long as you mount the usbdisk correcty. Maybe you can even change the permissions after you mount it but am not sure. Hopefully somebody on LQ can confirm this. After you mount to change the permissions I would try a chmod 755 /dev/sda1 or wherever it is mounted.
I am using sda1 in this example but I dont know what your usbdisk is mounted under, dmesg should tell you.
To mount it and have non-root access to it try as root from terminal.
mount -o rw exec uid="your user id" gid="your group id" /dev/sda1 /place/to/mount/usbdisk -t <the filesystem type>
for a better understanding of how this works or check out this webpage