Hi, Rich.
If you are using a CA- licensed Realtor, they will be using a CA BRE residential purchase agreement form. On the is a check box that says you will be making an all-cash offer with no lender financing needed. That was put on the form a few years ago specifically because people were saying it was an all- cash offer but having to get loans. Basically, people were lying and sellers got sick of it.
If you're not using a realtor, you can put whatever you want, I would guess. But you wouldn't be able to put in any contingency for getting the loan. So if the loan didn't come through, or for that matter took longer than you have said for a closing date, you would have no recourse for getting out of the contract based on that.
Also, what are you going to show the seller for proof of funds? In California, it is usually requested, same reason now as the all-cash offer deal. People used to say sure,, I got it in my pocket. Than not close the sale because they didn't qualify, etc.
Lastly, not telling your commercial lender is not a good idea. In residential lending, people are told not to buy ANYTHING on credit until they close on the house, because it changes FICO scores and DTI ratios. I will say I'm not sure about commercial lending since it's usually not based on your personal credit, but something you might not want to risk.
Feel free to do what you like, but I personally would not suggest that course of action in California. Just a lawsuit waiting to happen.
Travis