I disagree that accepting crypto to your hardware wallet while running a business is a good practice, this is the advice that my long time crypto investor friend was telling me when I told him that I want to start accepting crypto payments in my business, we argued for a while and I got tired.
When it comes to business related, I would assume that transactions will be done frequently, which means you will both send and receive. Business wise, I will advice Hot wallets ( the non custodial type). My reason is because: I know that the funds won't stay there for a very long time, so it's ideal to save it in a place where I can easily move it out. But if the amount happens to be very huge, I will advice that you use the Hardware form and endure the time taking to move funds out. It's better to waste your time trying to move your funds, than to put it in a place vulnerable to attacks.
Aside that, it's very important that we understand the difference, so as not to involve yourself in unnecessary arguments.
A hardware wallet are also known as cold wallet is basically are an offline wallets that are connected to external applications only. They are used in storing private keys which allows a user to access his/her funds. From the ones I have seen, they are usually in forms of a USB. I keep advising that Hardware wallets should be considered for
long term hodling of Bitcoin. I think we can only classify this types of wallets as non-custodial. Some can be time wasting.
While Software wallets are also known as Hot wallets are usually connected to the internet and come in the form of desktop, web and mobile wallets. I think custodial and non-custodial falls under this type of Wallet, as we can have a software wallet that can either be a custodial or non-custodial.
I personally use the software wallets (non-custodial in particular) as they are less expensive than your hardware wallets.
So I think you are right by stating that -
Hot wallets are good for day to day transactions, activities that involve solving tasks to make more tokens like testnets and airdrops, connecting to uniswap and other Dex for purchases, in the end you move your valuable assets into a hardware wallet for a long term safekeeping.
But you should choose the non-custodial to be on a safer side.