All-in-one bathtub

I've been thinking about a cold soak solution, but I have limited space and can't do any hard plumbing. I asked the salesman if there was a way to install a cooler on the existing bathtub. Any advice if so? Because I just want the hoses to be submerged in the water, not close to the pipes, so they told me it was possible, but I had to make sure they were completely submerged. It's a dedicated bathtub that I wouldn't use for bathing, which makes it so much easier. My salesman recommended me a suitable ice bath machine and gave me suggestions for installation, he was very friendly and patient, now I can use it normally, thank you very much!