I would say you probably won't need an EP as your company are not in Singapore. I'm not sure you would get one anyway unless they have an office here. I also presume you will be earning your income in HK?
I think you may also have some trouble getting an apartment without EP, but you could try a
Serviced Apartment. I think you could come in on a normal Visa, extend and then make a Visa run to JB. If it is just a straight business trip, I don't think it's a problem, we have many foreign workers coming here for projects and the never get an EP (some stay for 1-2 months) as none are employed by our Singapore office.
Obviously, i'm not saying anything above is fact and I would also recommend you check all of this out. However, don't rely on HR; I have never seen a HR department in the world that is any good and you are the one that gets in trouble if they are wrong. I would get them to arrange/inquire and then validate the information you receive yourself.