The time frame could limited through countdown clock or classroom timer resources, allowing them a limited time frame to complete their website searches. As well, using the Socrative resource to develop specific questions in the format of a webquest will provide students with more direction than simply setting them loose on a website to do research and perhaps engage them a little more in the correct topic. In terms of oversight, a site like Screenleap or Jog the Web might allow more screen-sharing so I can see what the students are doing while they are doing it, allowing me to help them with their work and be sure they are focused on the correct site. (Mind you, this is what I see from a quick glance at these sites).