MikeAlpha,
There are a few training centers in the US that will train "off the street" pilots for type ratings. One just south of DFW airport has been the first stop for pilots hoping to get on with Southwest as they used to require a 737 type before you could interview. (Now they will hire you on the condition you get the type before their training starts.) I've seen prices around $7000 for the 737 types. They do some other rating too, 727, DC-9, 757-767. And there is is a company in Miami that does lots of training.
It will look the same on the certificate no matter how you got it - B-737. If you go for the PIC program it will just say B-737. If you go for the SIC program it will have "B-737 SIC privilges only" in the limitations section.
Apply? Most training centers have FAA Designees on staff so you could end up doing the oral or the checkride in front of a Desiginee, in front of a Fed or in front of a Fed watching a Designee. The paperwork all goes to Oklahoma City.
I've been doing a bit of systems instruction for the above company and they have had some students recently getting the PIC rating because their CAA/DGCA/FAA wouild not validate an FAA SIC type to the local certificate.