Are we allowed to send/receive wires from Non-Cooperative countries provided on the list from FATF?

Yes. You are required to be aware of your activity with these countries, because presumably their AML controls are not up to standard, but you can conduct business with those countries.

The countries that you may not do business with are the US Sanctioned countries.

Note that some on FATFs list are on the US Sanctioned list.

To ensure appropriate due diligence, you might want to have a process to identify and escalate for review prior to processing these wires. EDD might include documenting purpose of the wire if this is not already part of your process, review of originator's/beneficiary's wire history, etc. Each bank has to determine what "EDD" will mean to them.