Skilled Worker, non-working spouse, tax savings

Dear Sir, I am on a Skilled Worker Visa (No Public Funds) and my wife is dependent on me. I'd like to know if I can save any tax by transferring some amount to my wife for her use since she is not working. I understand that I have no recourse to public funds, hence I wouldn't like to think of applying for any benefits.

Hi

No.  Only you are taxable on your income.  
You cannot transfer some of your income to your wife for her to be taxed on it.  
If your wife has no income and you are a basic rate taxpayer, your wife can elect to transfer some of her personal allowance to you.  
Your wife must submit the request.  Have a look at the guidance at Marriage Allowance

Thank you