What will my mortgage rate be if I float it 30 days and then lock it?

I will be signing a 60 day contract, but do not wish to lock my rate until I am 30 days in. I am hoping the rates will not fluctuate too much so my 30 day rate will be less than my 60 day rate. However, my real estate agent said I must choose a lender in the first 5 days after the contract is signed. If I do that then doesn't the lender I choose have the upper hand to charge what ever rate they want since I am now obligated to them? I understand the rate is based on the market, but how would I know if the rate I am getting is the best the lender can do. They essentially can just say this is the best we can do and I would be stuck. I (buyer) cannot shop the rates to get the truly best rate.

Read more: What will my mortgage rate be if I float it 30 days and then lock it?