A pedestrian is generally someone who is walking along a street. Pedestrian can also be used to mean 'at a slow pace', such as, the trains movement was rather too pedestrian for Peter, so he took the plane. A walker would generally be someone is walking in the countryside.
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Adrenochrome you might wish to consider 'strolling' or 'ambling'. If you were writing about the 1920s, we used to use the word 'promenading'.
'Strolling' might be best suited for the passage you have included.What ever happened to "perambulating"?
Adrenochrome there do seem to be a lot of single women pushing prams around the park nowadays*** bless them, every one! [A]