The actual slider is a link-element you should be able to define a css selector based on its classes.
<a class="ui-slider-handle ui-state-default ui-corner-all" href="#"></a>
The first you find is the left slider, the second the right slider.
I have successfully used use the Action Builder and the MoveToOffsetAction to drag a slider X number of pixels into a direction. I would only do this if you need to verify an event fired during the sliding.
I think its a jQuery best practise to put the slider component in to a div with an id. If your slider does not have an id, urge the developers to give it one. Note the draggers have no id and can only be found in the slider compontent div on its class.