A bit of custom dialplan would probably work. /etc/asterisk/extensions_custom.conf in the [from-internal-custom] block:
exten => inboundpark,1,Park(default,s)
replacing default with the name of the parking lot from /etc/asterisk/res_parking_additional.conf if you have more than one lot.
Then add a Custom Destination with the Target string set as:
from-internal-custom,inboundpark,1
and finally point your inbound route to that custom destination.
The key is the s argument to Park which silences the announcement.