Yes, a confirmed diagnosis is a good idea - pine wilt is quite uncommon outside of the midwest and I'm sure your local extension office would be very interested if this really is the cause of the tree's demise. They should be able to ID for you as well or direct you to a certified arborist who can.

Regardless, this disease is vectored by insects (pine sawyer beetles) that transmit the damaging nematodes and if the insects are not present in the wood chips, there is little chance of infecting healthy susceptible pine species:
Is there a risk of spreading pine wilt in infested
wood chips? Yes, but it is minimal. Research in
Vermont showed that it is possible to transmit the
nematode from fresh chips to a young Scots or white
pine seedling, but only if the chips are placed in
direct contact with wounds on the sapling. Using a
few simple precautions, you can safely mulch
susceptible pines with chips from pine wilt-killed
trees. First, pile the chips for at least 6 weeks; the
heating and drying will kill both nematodes and
beetles. Second, avoid piling chips against tree
trunks when you mulch, and donÂt mix the chips
with the soil when planting new trees.
Iowa State Extension Bulletin

Here is a link that might be useful: pine wilt

Thank you SO much, gardengal! I will definitely contact the local co-op and see if they can ID the problem for me -- luckily I know someone who works there! And I'm thrilled to know that I should be able to salvage any chips (assuming that the tree is dead and must be removed)... there are no other pine trees in the general area, so I don't think there will be a problem at all.

Thanks! :)