Yes. Antiseptics weren't really a thing until Joseph Lister (for whom Listerine is named, though he wasn't involved in developing it) published his paper on the subject in 1867. Prior to the. The miasma theory prevailed. It's hard to pin down when his methods would e become widespread, but something set in the 19th century could easily not depict cleaning an injection site and still be pretty true to history.

Stuff like that makes me glad that I live in the 21st century.