Certainly now worse or less honorable than dodging a draft.
Nothing is more honorable than dodging the draft.
Why?
If a country enters a war that fails to inspire
soldiers to volunteer, & uses conscription,
that is a country unworthy of service.
To invade a country, kill people, & destroy
things without valid purpose is utterly wrong.
Russian draft dodgers are today's heroes.
(Even though you'd prefer that they kill
Ukrainians in that "special military action".)
If a doctor is writing a note, why would you presume the person lied? Is it really a false claim of medical need?
This is really just because of the cat's circumstances.
To get a doctor to prescribe medical need would be fraudulent.
Methinks that you & I have different morals.