There are a couple of lenders that can finance borrowers with a 600 score but the requirements can be a little more restrictive which makes it more difficult to qualify and limits you to just a few lenders.
If you were to work on raising your scores (with a mortgage professional's help of course) you would have more lenders to choose from and improve chances of getting approved.
As a retired Vet, you really should take advantage of your VA benefits and go for a VA loan.
This article talks about getting a refinance- http://www.brickhomepartners.com/buy-a-home/refinance-things - it may be helpful.
You'll want to focus your efforts on getting a VA loan and work to find a lender in your area who will accommodate a 600 credit score. There may be a few. You can also consider working with a credit repair service to address the items on your report that are keeping the score down. If you need a referral for either the lender or the credit repair service, please let me know.