Putting switches/relays after the DAC output stage to select between combined outputs

I'm looking at building a DAC based around the 8-channel ES9039. One of the features to boost performance is combining the channels, which I would do after the output stage i.e. the op amps.

I'd like the flexibility of having all 8 channels, but there could be occasions where 4 channels would be enough, in which case I could make use of the unused channels by combining pairs of channels together.

Some of the ESS evaluation boards achieve this effect using headers and jumpers, but to be useful to me I'd want to be able to use a switch/relay of some sort. I am, however, cautious of adding anything in the way of the signal path. Would the performance improvement of combining channels be reduced by adding something like a relay to the signal path?