Automation is my solution.
There are plenty of automation apps, but I use MacroDroid, since it is easy to learn (that's why I use it) and the behaviour can be easily customized to get the result you want. Besides,free version allows you to create up to 5 macros and so for the task at hand, free version suffices. I prefer automation as a first choice when I need to get something running the way I want rather than depend on an app.
MacroDroid uses macros to perform desired actions.
Macro for your requirement would look like this:
(I am thankful to OP for testing o on his Lollipop based device and confirming behaviour as expected, since my device runs on KitKat and Google has implemented API level changes differently in Lollipop)
Main Macro (working as tested by OP)
Application Launched → Google
Volume Change → Configure
Here you get 7 options which can be chosen singly or in combination on a sliding scale from 0 to 100. Options are-
5. System Sounds
6. Voice Call
7. Bluetooth Voice
Choose ((2) Music and (5) System Sounds) and set them to 0 for Lollipop
Choose ((3) Notifications and (5) System Sounds) and set them to 0 for KitKat
( Reason for different selection is explained in Note below)
You can set the (6) Voice call level as desired ( select by testing voice
typing comfort level)
(Macro runs only when constraint is true, so here it runs always)
Save the macro and ensure it is enabled before testing
Optional Macro (Awaiting OP to test)
(In case you need to change volume manually for voice typing, the "ding sound reappears, as reported by OP. This macro is to kill the "ding sound". This macro is not required if you are fine with the voice control level in the main macro and do not need to manually change voice typing volume)
Volume Button Pressed → Volume Up → Update Volume
Volume Button Pressed → Volume Down → Update Volume
Action and Constraints
Same as in the main macro
( Triggers work as logical OR and the action for muting the "ding sound" is triggered whenever the volume is manually increased or decreased for voice typing )
Why this should work for everybody
My search hasn't shown an app or Xposed module that can do this ( not denying the possibility, though)
This macro doesn't require root unlike Xposed approach.
Granular control on different Volume settings. MacroDroid permits you to alter sounds, with a flexibility that is beyond what normally is available in ringer / volume sound control as this example illustrates. My Huawei Honor 6 has only 6 types of volume settings (which is more than some devices offer) but not Bluetooth, which can be controlled through a macro
Customization. You can set "modes", which are like global variables akin to setting profiles. As an example, you can set this macro to run while at home (by mapping cell towers of your home location) and have the "ding" sound active elsewhere. Possibilities for customization are pretty much as you wish
Last but not least, it is free :-)
Do not Greenify MacroDroid and exclude it from task killers, if you use them.
Enable MacroDroid in "Auto Protect"(Huawei phones) or "Stamina Mode" (Sony phones or "Power Nap" (Stamina Mode Xposed module for non Sony devices). Also, if you update to Marshmallow in the future, exclude MacroDroid from Doze. Refer this: Is there a way to exclude an app from Doze?
These features prevent app(s) to be active when the device is not awake, conserving battery. May not be pertinent to your phone but adding this as a general precaution.
Enable MacroDroid in accessibility settings and also allow it as device administrator in security settings.
For Lollipop, enable notification access from notification settings
Google Voice Recognition functionality that creates the "ding" sound was streamed as notification stream in KitKat. In Lollipop this is switched to music stream. Hence, in the macro, settings differ.