I have a host that is on the inside of a virtual context and I need to do the following:
for only UDP SNMP response traffic, use a specific IP RFC 1918 address on the outside interface of the context.
for all other traffic, use the existing PAT internet-routable address on the outside interface of the context.
the primary reason for this setup is because public addresses are limited and I don't want to use straight PAT translation because my monitoring host will consider all of the hosts behind a context as a single host.
Maybe you can try Policy NAT.
But if the packet will be sent to internet, it might be dropped if its source IP is a private IP.
I would like to suggest you to setup a vpn tunnel so that you can keep using the private IP.