The FT-70DR uses the same microphones as the FT-60, including the SSM-17A that you seem to have missed. The plug looks to be a 3.5 mm TRRS. The FT-60 is a common HT that has been produced for years, and there should be lots of accessories for it. It's not clear if the FT-60 and FT-70DR use dynamic or electret (condenser) microphones, but most radios these days tend to use electret microphones because they're cheaper and work just as well for HTs.
You should be able to find nearly any type of headset or hand microphone you like that is compatible with the FT-60 and FT-70DR on the accessory market. But if you don't like the available accessories then it shouldn't be too difficult to wire up an adapter cable or adapter box to use a headset or microphone with a different plug; such an adapter may need to supply amplification or attenuation, and bias voltage for an electret microphone.
You could also find a microphone or headset that uses the older two-plug standard used by that CT-44 adapter, with one plug 3.5 mm and the other 2.5 mm. I tried to quickly find a diagram for the wiring for that standard for Yaesu radios, but couldn't. I know that other manufacturers (Baofeng comes to mind) use a similar double-plug standard, but there is no agreement between manufacturers for microphone standards, so beware: a microphone that works with a different manufacturer's radio and physically plugs into the CT-44 adapter may not work, and might damage the microphone and/or the radio. Personally I wouldn't bother with that annoying adapter; I'd just find a microphone or headset with a TRRS plug that is made to work with the FT-60 and FT-70DR.
When looking for accessory microphones or headsets, your best bet IMO is to contact a well-known amateur radio equipment retailer. They are likely to sell you something of reasonable quality that will work with your radio. The manufacturer MFJ Enterprises makes a variety of accessories, but they have a reputation for erratic quality. (I have an MFJ speaker/mic that works fine. I have no association with MFJ, except as a customer.) Then there is the army of sellers on eBay, Amazon, Alibaba, etc., which sell at low prices, but buyer beware: there is a lot of out-and-out junk out there on the market, and lots of products that are advertised as being compatible turn out not to be.