The software currently doesn't allow selective probing of a design, but it is something we've heard a lot of requests for. It's definitely something that we'd like to get around to implementing.
For the moment, what I would recommend is either:
1) Create a new gerber file with only the part you want to paste.
2) Edit your existing gerber file to remove everything except the part you want to paste.
If you're trying to lay down paste for a number of pads with components mounted in between, you'll need to repeat this process for each set of pads - otherwise the probe will move and be knocked off, as you mentioned.
Hope that helps!