In english it is also acceptable to say... Are we trying to not age?
Yes, it is acceptable. On the other hand, some people feel it is bad style to "split" the infinitive by inserting words between the "to" and the root verb.
Even so, I preferred 'Are we trying to not age?'. I am pleased Duo accepted. In both cases, not would get a verbal stress.
"Are we trying not to age" and "Shall we try not to age" have different meanings in English. Whether both are acceptable translations from the Czech original, I don't know. Maybe a native Czech speaker will address this in the future.