I looked into it.
From https://mods.factorio.com/mod/InstantCrafting (factorio v0.16)
Known Issues :
Incompatible with HandyHands.
So I'm guessing you are using https://mods.factorio.com/mod/Instant_Crafting (for factorio v0.17).
That mod is deprecated, which means it has been abandoned by the author.
The way InstantCrafting works is it cancels any handcrafting you start and gives you the results immediatly and removes the ingredients from your inventory. HandyHands pauses automatically if you cancel handcrafting anything started by HandyHands so that you don't have to look up the pause button for the mod if you don't want to handcraft it so HH doesn't just instantly add anything back to the handcrafting queue when you cancel it.
I would say that InstantCrafting is "poorly written" in that it works in a way that doesn't utilize factorios native handcrafting system. I would say it's a problem with InstantCrafting and not HH since the limitations of the mod API means I can't detect how a craft was canceled and they tried to "fake" instant crafting by going around factorios handcrafting system even though it already has the capability to just speed it up incorporated in the API.
I think I've seen mods that speed up handcrafting with research so it should be possible to make handcrafting effectivly instant in a better way.
searches
I did find a mod called magic stick though https://mods.factorio.com/mod/Magic%20Stick
It gives you effectivly instant hand mining. It should be easy to change magic-stick.lua in that mod and replace mining with crafting to get your instant crafting. I can test it later.
searches more
I found https://mods.factorio.com/mod/realvictorprms-crafting-miningspeed-research
a mod that does the same as magic stick but more balanced and fro crafting and mining. But it confirms that the change from "character-mining-speed" to "character-crafting-speed" in magic-stick.lua would work.
I haven't tested it by here's my modification to Magic Stick https://forums.factorio.com/viewtopic.php?f=190&t=68870 that gives you effectivly instant handcrafting after a research that requires 1 red science pack.