If you take out a 2nd mortgage, the interest *should* be tax deductible provided the money is actually used for improvements to the home and not diverted to other uses. You would need to check with your tax advisor/CPA regarding the specifics of your situation. That being said, you'd be paying those higher interest rates just to get a likely small amount of taxes deducted. It will end up costing you more than paying cash, regardless.

Paying cash = no interest charges, so you know the total cost immediately. Unless you can invest that cash and get a higher % return than what you'd be paying in loan interest, paying cash is the most cost effective option.

That being said, it sounds like you would be cashing out stock investments in order to get the funds, not just withdraw cash, so you also need to look at any tax consequences from liquidating those investments to pay for the renovation. If you're selling investments held in a taxable account for a gain, then you'll be incurring tax liabilities and need to account for those in your planning.