There is no rule, as far as I know, that indicates that Use Magic Device, Disable Device, or Sleight of Hand require hands in order to use. In every case, there are uses for the skills that do not require hands.
Being a quad base form doesn't mean you couldn't have fine manipulation. Some animals have prehensile digits on their feet (apes) and dragons have always had fine manipulation with their claws as far as I know (old draconomicons etc.). Unless you put something like hooves on a particular set of limbs I would be hard pressed to see why it couldn't be done with them.
My serpentine eidolon has neither feet, nor hands, but is quite adept at fine manipulation using its tongue.
My serpentine eidolon has neither feet, not hands, but is quite adept at fine manipulation using its tongue.
You dirty dirty dork...
You could always just give the quad eidolon arms anyway...
Even if you ruled that fine manipulation wasn't possible without arms and hands on those arms, Use Magic Device has plenty of uses that aren't depending on fine manipulation (it doesn't take fingers to fake an alignment so you can wear a Robe of the Archmagi), Disable Device is vague enough that it doesn't really say HOW you are disabling traps or sabotaging devices, and sleight of hand similarly is up to your description for how you accomplish its uses (it's not all pickpocketing- it also includes hiding an object on your body, and so on).
