Thanks for the links.
The DD50 owner's manual isn't in English. Do you have a link to one that is?
I'll preface my comments by saying that my electronic music experience is narrow and out-of-date. I'm trying to help but I may have made some wrong assumptions.
Here are three relevant quotes from the HH65 owner's manual (emphasis mine):
"When used in conjunction with a pad such as the TP65, etc. as the hi-hat pad, it is capable of providing operation and tone that comes extremely close to that of an acoustic hi-hat, from fully open to fully closed and more."
"Changes in the sound produced by the hi-hat pad can also be obtained according to the amount that the HH65's pedal is depressed (close/half open/open)."
"Sensor System: Continuous Switch x1".
These statements are contradictory. Does the HH65 report its exact position or foot pressure, so the sound of a partly open hi-hat can be simulated continuously over the full range? That is, tightly closed, gently closed, slightly open, half open, fully open, and everywhere in between? Or does it just report three possibilities: closed, half open, fully open?
If the former, the HH65 pedal contains more than just switches; it has a potentiometer or pressure sensor that requires a voltage on one cable connection and produces a variable control voltage on another cable connection, according to the pressure on the pedal. If the latter, it probably just has two switches. Both possibilities are consistent with a TRS cable.
(Since it uses a standard TRS jack cable, I very much doubt that it uses MIDI.)
That's the first question.
The second question is, what capabilities does your drum synth have, and is it compatible (at all) with a hi-hat pedal that reports the pedal state as either (a) one of three possibilities, or (b) a continuous voltage representing the pedal pressure?
The drum synth may only support a simple ON/OFF signal on its hi-hat pedal input. In that case, you may be able to use the HH65 with it, but only as an ON/OFF pedal, so you wouldn't be able to use the cool HH65 features.
I haven't downloaded the DD50 technical manuals because I don't trust MediaFire enough to let them run their scripts on my machine (this is part of my plan to avoid malware, which has been successful so far). If you can upload them to the other site, I can look at them and I may be able to answer the second question.
You may be able to answer the first question if you're prepared to open up the pedal and take some photos of what's inside. I'm mainly interested in the component in the top of the box with the jack socket, that is pushed down by the flexible finger that's attached to the bottom of the moving pedal at the front. I think it's a pressure detector. I would like to know the part number, if it has one, and how it is wired to the jack socket.