You should definitely call your current lender about refinancing. Coops have not lost as much value as SFR in Queens, so your LTV should be okay for your Board to sign the Aztec. Just don't be surprised when they don't know what a coop is. If they give you closing costs over $3,000 then you are definitely speaking to someone who doesn't know what a coop is. Also check with your managing agent to see if the coop would come to the closing. If they do find out what their charge is and where the closing must take place.
Like Scott says, compare what your current lender can do vs. what a new lender can do. Your existing lender may be able to handle the CEMA process for a reduced cost (Google "CEMA mortgage" to find out more about CEMA if you don't know it), making them a better deal in terms of lower overall cost.
Even if you don't have 10% equity, if your loan is owned by Fannie Mae or Freddie Mac then it may still be possible to refinance (up to 125% of your home's value) using the Making Home Affordable Refinance programs. http://www.makinghomeaffordable.gov/get-assistance/loan-look is the link to check if Fannie or Freddie own your mortgage.