I match the pad width to the hole size and ignore EPC error message, or make the pad size the same diameter as the screw head. (e.g. M3 screw, 3.2mm hole, 6.5mm pad diameter to match M3 nut "across the corners"). Latter helps layout as it creates a no go area for tracks/components and assists with complying with creepage/clerarance distances.
Usually the manufacturer will understand when a hole with no annular ring will be a hole .... Especially if there is no connection to it. Normally if there is a query they would contact the client to verify.
Not related, but do watch out for cheapo pcb manufacturers who will alter clearances to suit their own processes, especially on inner layer clearances ...... And that can cause a board to fail either functionally or from an established EMC spec.
All good manufacturers will contact you to check first if they need to alter any part of the gerbers