Can i use Smal motorcycle battery on a big motorcycle?

I have honda cbr 500f with a 100 percent dead battery and my question i can i use small 4 ah battery from my scooter on it, will it overcharge it or damage the voltage regulator or the alternator, do i have anything to watch for? (even if the small battery can't start bike i will give it a push…, I'm interested will it work)?

Added (1). Ok so the reason for the old battery failing was that the voltage regulator failed and shorted the battery, Now i mounted a new one, Bike starts fine with the small battery and it recharges fine but it overheats the new voltage regulator after a minute of running on idle. I even tried to add a ground line directly to the battery and it still overheats

New regulator ->> http://extraimago.com/image/1G1
Old Regulator ->> http://extraimago.com/image/1GE

If your motorcycle starts up without a lot of cranking, the small battery will work. Will recharge just fine after the bike starts.

O Are the two batteries the same voltage?

Even if it doesn't have enough cranking amps to start the bike, it should keep it running if all else is OK.

All else is NOT OK if the new regulator is heating.
Further diagnosis/repair required.

Run it as is and you will be buying another regulator in addition to the other failed parts.