There is no phase shift on the phase-to-phase voltages. The voltage at terminals V11-V12 on your synchronizer is in phase with the voltage on V21-V22, even though the one VT is wye and the other is open delta. Phase-phase voltages are the same.
But you need to verify that the synchscope, the synch check relay and the synchronizer all can work with different phase-to-ground voltages on the secondary. If the open delta VT has B phase grounded as is normally done, the A & C inputs will be 120V phase to ground (assuming the VT ratio gives 120V phase-phase). The wye-wye connected VT's will have 120 V phase-phase but 67V phase to ground.
The synch equipment has to monitor and control to phase-phase voltages, not phase-neutral.
As long as your relays and wiring isolate the inputs and don't try to use a common "neutral" or ground reference point it will work. If the wiring has one side of the synchscope and synchroniser common to both VT inputs, you will blow fuses on B phase. Insert a 120:120V isolating VT if that is the case.
If you do put an intentional 30 degree phase shift in the VT circuit, you will synch 30 degrees out of phase and possibly damage your generator or worse.
We have successfully used the wye-wye VT's on the bus and open delta VT's on the generator many times. It is a standard design for the GE 7F gas turbines.