I had someone call recently about what I would recommend for a pet safe weed killer. A bit of veterinary information network (VIN) searching verified what I was taught in veterinary school.
Most weed killers are really mammal safe. Of course, if you think about it, they would have to be because humans are being exposed to them too. The danger in weed killers is probably more about the other ingredients than the active ingredient anyway. Active ingredients usually target things only plants have. For example Roundup (glyphosphate) targets the shikimic pathway involved in photosynthesis- obviously not going to affect humans. Of course the other part of that product helps it stick to the plant so that part could cause some issues if ingested directly.
Bottom line on most weedkillers are spray what you need to, let it dry, and then let your critters out and don’t worry about it too much. Of course, always store the bottles where your pets cannot access them because the toxicity increases in higher concentrations (straight from the bottle).
And anyone, human or pet, can have a contact allergy to just about anything- so itchy paws may be an idiosyncratic individual reaction and washing the affected paws w warm soapy water will help decrease reactivity.