Deepika, the hand mixer is not really good for making soap. you need something that does what the Preethi / Sumeeth mixers do but should be immerrsible in the oil and lye mix instead of the liquids going in the jar. If that is not available, you should just be ready for long mixing times. Soaping at higher than room temperatures will likely help. I would be really careful mixing with the hand mixer as, number 1, there is a bigger chance of everything splashing around which is dangerous, this is the reason why I am not suggesting that you put it in the mixie jar and give it a go. Number 2. most hand mixers will die out before getting that thing to trace. Your best bet would be hand mixing and lots of elbow grease.
I don't know if you could salvage this batch. Its a small batch so not much in terms of wastage. May be you should try finding a stick/immersion blender and come back here before you plan your next batch so you could double check.