I'm not aware of any UNIX that will allow you to have 19200 files open simultaneously; it's possible the situation is different under Windows, but I doubt it. In a quick test, I can open 1020 files before my script dies with a Too many open files error.

Workarounds include storing the filename in the hash, opening the file before using it and closing it afterwards; do the same thing, but cache open filehandles, and upon receiving a Too many open files error close the least-recently-used filehandle, and jot down somewhere that it needs to be re-opened; append the data to the hash entry, itself, then go through all hash entries and print their contents to the appropriate file.