For vision screening, it is usually done via a task more than a questionnaire, it is called visual search task, a simple task that is enough for visual screening, these 2 links are helpful:
If you are interested to know if your subjects can see to do the computer based task, you could simply have them read similar sized text on the computer or a tablet, as you will be using for the cognitive task. It sounds like your concern is simply, can they see to do the task on the computer. If that is the case, this would be the fastest and easiest way to sort that out. If they cannot read similar sized text, than they won't be able to do the test.
Perfect. You could use a near point reading card or simply have them read on the computer monitor. If they can read there, they are ready for you to test them.