Can you execute sqlite3 outside xbin directory?
If you've got the binary available, you could upload it to your device and use it from there. Note, however, that this won't work from SDCards – but the following approach should do without rooting:

adb push sqlite /data/local/sqlite
adb shell "chmod 0755 /data/local/sqlite"


Then you can always invoke it using the full path, e.g. /data/local/sqlite somedatabase.db, from within a terminal app or adb shell session.