A microusb mouse may work, but it depends on the version of android your phone runs. You could also connect you phone to a computer as mass storage, but I don't remember if application files are accessible that way. You could use adb (the android debug bridge) to get the file off as well if you have debug mode turned on, the instructions
here may help (and you might not need to root your phone either, try it without first).
There are several options (as long as you don't try to reinstall the app), so your bitcoins are almost definitely recoverable. Always remember, backups are important!