I have been told that we should ignore waswasa (or baseless misgivings), but I do not entirely understand what that means. Does it mean we should avoid doubts that are so small and implausible?
For example, if I gift someone with a knife, he may use that knife to hurt someone else. Therefore, I avoid giving him the gift
Waswasa means whispering of shaytan. He is our staunch enemy and he wants to keep us grieved at all times. He never wants to let us stay in peace. Any feeling of sin or evil is from shaytan or from our nafs (ego).
We should have the ability to differentiate between ilhaam, which is from Allah, and waswasa which is from shaytan.
What you have mentioned is correct. Small doubts should be ignored. The doubt about knife is just paranoia, so ignore it, unless you genuinely feel that the other person would do something stupid.
May Allah help us get rid of waswasas and protect us from shaytannir rajeem.