Well, I am a little confused. You must be speaking of a winterized raw water system left filled with antifreeze for winter, since you are in New Bedford, Mass, right?
So don't worry. Let whatever antifreeze will drain out, drain. The raw water components are made of robust metals and won't be harmed a bit. Do make sure that you elevate or plug the tranny oil hoses so they won't drain oil.
You say you are jumping into the tranny cooler first. Yes, that is one of the easiest but also probably the one least likely to need service. If the after cooler never has been serviced it needs it the most as the consequences of failure are severe. Search for articles on this forum about after cooler servicing (I originated one on the Yanmar 6LY) and read Tony Athens articles on servicing the Cummins aftercooler at sbmar.com. Here is a thread on the 4LH: http://www.trawlerforum.com/forums/s...ace-34019.html
And if you are ok removing the after cooler but are leery about disassembling, cleaning, reassembling and testing them then Seaboard Marine at sbmar.com will do them for a reasonable fee.