Shoes for wet muddy school walk, that are not too frumpy

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As per title, I need some shoes to wear generally out and about, in bad weather, it gets a little muddy around here in autumn/winter. Ideally they need to go fast also, as I need to outpace 3yo DS, who is quick and flighty, with no road sense.

Ideally I need something that laces up, as I have skinny ankles but wide toes, but realise that laces probably equate to frumpy.

In practical terms, something like this would be ideal, but I'm sure I can do better than this in terms of looks:

waterproof trainers

I covet these boots, but would prefer to spend less, and they probably wouldn't fit, and I like to wear blue jeans, so on every level these are wrong, but I aspire to their style:

posh waterproof boots

Any ideas please?

Posh wellies? Seems the fashion now to wear wellies as proper footwear.

Check out keen boots and trainers quite sporty but some our quite cool too ( can be pricey?)

Why not just stick posh wellies on until it dries up? Hunters are comfy. Or joules? And spend the money you save on a pair of converse or something to wear when less muddy?