Yes, you'll want to refinance.
Whether to cash out is a personal decision, and is just another iteration of the "pay off your mortgage early vs invest" debate. Personally, I'd probably refinance the $156k to lock in the low rate.
When I was poking around the idea of refinancing a few months ago, I noticed that I could get a lower interest rate with a $200k loan vs a $100k loan. So even if you want to keep your mortgage balance low, you may want to consider getting a cash-out (and larger) mortgage, and then using the cash to pay the balance down to where you wanted it to start anyway.