Well the real WK is multiple units all the way, currently Class 777 EMUs, so the DMUs won't look completely out of place! However blue-grey livery EMUs would have to be 503s...
Of course, on Merseyrail, DMUs did get as far as Bidston (for Wrexham) and Rock Ferry (for Chester) !
Thinking of an alternative history, if the Birkenhead to West Kirby and to New Brighton has not been electrified by the LMS in the 30s, and the line escaped being Beechinged, then DMUs may well have worked into Birkenhead Park from WK and NB to interchange with the Mersey EMUs.
There might have been some use for Class 73s to do the whole WK/NB to Liverpool run, changing from diesel power at Park to run under the Mersey on electric power. At one point Merseyrail had some 73s, on Sandite duties, I believe...