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I would suggest using Sedgwicks leather feed. Rub it well in when everything nice and warm and it has softened a bit.
It won't bring back the shine, but it will protect the leather and keep it supple / prevent it cracking. Leave it for a few days, then polish with boot polish in the normal way to smarten them up if you want.
Lennon also do the these Rufflander boots for workshop use. £59.95. Hand made. Impervious to most workshop chemicals and dropped hammers. I've never polished mine, as the impervious surface is impervious to leather treatment too.
Feel like @adroit and @pdlouche are too guys that could help here