I think it is possible to do it (although I agree with Sysexpert that correct way is to use DNS forwarders on your Windows servers handling DNS. )
I can think of two two ways of doing it.
1) Lets say you have two NICs on the server. One is enabled, one is disabled. Windows would use DNS settings on the Active NIC. Domino would use DNS on the first (!) NIC which does not have to be active
Open "Network and Dialup Connection" folder, then click on Advanced-Advanced settings. in the Advanced settings window, using "up" and "down" arrow buttons, rearrange connections to put connection (again, it does not have to be enabled) with DNS settings for Domino on top of the list
2) Using \HKEY_LOCAL_MACHINE\SYSTEM\CURRENTCONTROLSET\SERVICES\TCPIP\PARAMETERS\NAMESERVER registry keyword.
If presented, Domino will use information specified in this keyword for DNS and would not use DNS settings from Windows.