I have an Ozeri milk frother that came with an attachment that looks like a propeller on a shaft. They call that attachment a “cocktail mixer”. Here’s the link:
https://ozeri.com/kitchen-accessories/Ozeri-Frother-Stainless-4-Frothing-Attachments/B00BISKPMG
I find that it works better than the frother attachment when I want to mix colorants into batter, but it doesn’t have any where near the power of a stick blender. If I’m patient, I can bring soap to trace and without adding air bubbles, but it doesn’t have the power to mix past that. It seems to be unavailable at this time, but I found this, which looks similar:
Rabbit Cocktail Mixer/Frother
More information:
https://www.amazon.com/dp/B0039PY3RE/ref=cm_sw_em_r_mt_dp_MH197TV9HRDE3T672A98
I assume the shaft on the Rabbit mixer is stainless steel and the color of the unit is “chrome” because chrome plating is not food (or soap) safe.
I watched a YT video last night where the person removed the coiled spring from a frother attachment, leaving just a stainless steel ring that he used to mix hobby paint in small jars. I have multiple frother attachments, so I might try it. As far as I’m concerned, frothers = bubbles in my soap.
I would love to get my hands on one of those Bosch mini blenders. I guess it might require a plug adaptor in the US.