prepay then refi on small loan vs. refi bigger loan with large downpayment

Hello!

I need help with the following situation and would appreciate some input:
I have 160k cash available
I have a 240k mortgage at a high rate (4.5%)

 

Should I:
a) pay down my mortgage immediately with 160k, then refinance on a 80k mortgage.
b) refinance immediately on a new 240k mortgage, using 160k as a bigger downpayment.
c) it doesn't matter

 

Thank you! Any help would be great!