"By a certain route" vs. "via a certain route"

Solution 1:

I see both as semantically correct. Both are used, according to ngrams for by a certain route,via a certain route, the latter less commonly.

My own rationale for not using via and a together is that two ə sounds together sound odd or require extra effort to say. (However, Wiktionary shows the sounds as being different: /ˈviːə/, /ˈvaɪə/ vs. /ɑː/, /a/)

Solution 2:

Though both usages are common, using 'by' is more ambiguous. 'by' can mean 'next to' whereas via always describes the traveling itself. So, if the route was 'a highway':

She traveled via a highway She traveled by a highway

In the latter case, her route could have only briefly led her next to the highway.