The problem is that one of these guys could be pulled over by VOSA for a routine check, and the VOSA guy may decide that he should have a card and refuse to let him carry on. I imagine that this would cause a good deal of grief for all concerned.
Any new employee, who took his car test after January 97, will have to take a test to get a licence to drive a 7½ tonner. (Cat C1 and Cat C1+E if they tow a trailer). I may be wrong, but I think that this will include getting a DCPC as well.
To get all the current drivers through the training before the deadline will not now be possible. You might consider that to avoid potential problems in future, it might be worth doing, even though it will be late. It's not cheap though - Five full days 'training' to get the certificate.