Yes, that's right.
It solves that situation but it doesn't help for future situations where I have more than one verb in a clause and I need to determine which verbs goes with which subject is what I'm saying but can't get across.
Do you remember 客が少ない２月と８月の１８日 in your other thread? I wrote "
since there are few customers in February and August" using your translation, but the literal translation is "the 18th of February and August when customers are few". Thus, it's actually ambiguous which, the two days or two months, there are few customers just from the structure of the phrase.
However, it's odd that there are few customers only on the 18 of February and August every year as a common sense, and it's relatively well known that customers are few in February and August in Japan. Therefore it's interpreted that 客が少ない only modifies ２月と８月 as a result of all these reasons.
Also, I gave you an example 持っているカバンの色 in the same thread. The literal translation of this phrase is "the/a bag's color I have", but we usually can't possess a color, so it's reasonable to interpret it as "the color of a bag I have" as a common sense.
However, as for 好きなカバンの色, it's ambiguous whether the bag is favorite or the color of the bag is favorite. It's impossible to get the correct meaning only from the structure of the phrase.
The same goes with ライバル店が人をたくさん集めるため、特売セールを行っています。. You already know that this sentence can have two completely different meanings, and the correct meaning is decided only by the context.
Back to the example ウイルスがついた手でドアなどに触ると, indeed ウイルス can be the subject of 触る from the viewpoint of the structure of the clause, but it's illogical since virus doesn't have their hand(s), as I already pointed out.
Actually, this is an important key. As I wrote so far, it's sometimes or maybe often impossible to get the correct meaning just from the structure of the sentence/clause/phrase. You need to use your knowledge, common sense, the context, etc. etc. to get the correct meaning after all.