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Some shoes (I think Dr Martens) recommend only mink oil. Not sure who else does boot-wise, maybe yours.
Considering their condition, same thing as I usually say for any dry leather shoe: The go-to is saddle soap to clean the shit out, and then start to add oils back into the leather. Cobbler's cream is magic stuff otherwise look for an all-natural leather cream. Doesn't matter if it's cheapo cherry blossom or timpsons or kiwi at this stage. If you fancy you can even use body shop moisturiser since if it's good enough for humans it's good enough for leather shoes.
In that condition you could go less-is-more with dubbin, but it can create a sticky mess if you apply more than the minimum possible. Takes a lot of time to get it rubbed in and drying. I put too much on a pair of Spanish riding boots and a month later were still sticky.
More useful actually, get Carr's leather oil. Same applies as dubbin, use as little as possible and be prepared for mess and drying time.
Avoid spray-on waterproofers or anything full of chemicals.
Please condition that leather though! Worn-in looks great, but leave em dry and you'll cut years off their life.