The following is "common sense" based on my own travels. Officialdom may decide otherwise.
If I was doing this I'd try very hard to get an official answer to this in advance and very preferably in writing.
I certainly would not trust only the advice of well meaning people like me on an internet site :-).
If you have a Singapore visa and the two flights are not linked, so that you recover your bags as of right between flights, then you should be able to take all your baggage (or just the bag in question with the rest in luggage storage) into Singapore airport public spaces, passing through Singapore customs* in the normal manner. Once clear of customs you can do what you wish with your baggage (subject to the normal laws of Singaporean society).
If you then check in with whatever luggage you have left you can pass through security in the normal manner.
*The "trick" here is customs and "normal manner". You would need to declare that the bag of goods is to remain in Singapore. Depending on contents they may wish to charge duty and may need to know its value. It probably does not matter to them whether the bag belongs to the other person or not. They will probably want to work on the basis that as you are carrying it, you own it. and charge you accordingly.
I'd imagine that there is some risk of this going wrong - if they cannot assess value you MIGHT end up losing the bag if you cannot provide a means of it passing from their hands into Singapore after you leave. If you do not tell them what you are doing and they then find you are doing other than they expected, both you and the bag may not make your next flight.
You need to be CERTAIN what is in the bag.
Saying no to "Did you pack your bags yourself" at Bangalore may cause problems.
Saying yes when you are not 101% aware of contents could be worse.
It MAY be easier and not overly dear to send the bag to Singapore from KL via a freight forwarder.
FWIW - I have found Singapore customs officers friendly and helpful. Last time through, travelling from India, I was carrying a potentially banned (in Singapore) item which I declared, and they were professional and helpful and I was allowed to proceed.