What you're looking for is, in fact, a fully furnished condo with all utilities included available for extremely short term lease. They are rather abundant in Makati city, but they will be advertised in random places.
These are investment properties maintained to fill the exact need that you have, and you will often be doing business with an agent of the owner (broker) who is paid a modest commission for sales and a monthly fee for the upkeep of the property. You're going to be dealing mostly with Craigslist / classified ads unless you happen upon a property that is managed by one of the larger property management companies.
It is not at all unreasonable to ask to pay a reservation fee up front and the remainder of the agreed amount prior to moving in. This protects the seller and you. You should also ask to see recent pictures of the property, and it would not be rude to say something like:
Would you mind including a dated copy of today's news paper in the photos?
Also make sure that the price includes:
- Electricity without additional deposit(s)
- Cable without additional deposit(s)
- Water without additional deposit(s), working hot water in the shower
You'll know right away if you're dealing with an accredited honest broker or some shady character trying to separate people from their money on The Internet.
Finally, it's rather common (and expected) for the receiving party to pre-arrange these things for you when speaking of business trips. It's much better if you can get someone local to do the research and leg work for you.
What I can tell you (because I live in Mandaluyong and work in Makati) is that the properties in the location you stated (walking distance to Ayala / Makati ave) are very nice, so your chances of hitting something good are very high.
On a closing note, don't forget to go to Glorietta mall (can't miss it), locate the movie theater and then look for a food shop called Tater's. Try the popcorn.