Woud there be any European language that does not know the prefix para-?

That seems unlikely to me.

If para- offends, perhaps 'krom' can be made use of.

Krom-doktoro? Krom-kuracisto?

By the way looking through NPIV, I noticed that asistento is not listed. But this word might convey a higher degree of training/professionality than a mere asistanto.

Asististo seems a very odd word. Does asisti always imply a degree of formal qualification, or job position - la studento asistis sian profesoron en la eksperimento?

Mi trejniĝis/staĝis kiel dentista asistento has a nice ring, likewise, medicina asistento - but maybe that is just me.

Wells has savhelpisto and paramedicinisto.

I would also suggest kuraca asistanto.

Asistanto as a professional assistant could also be applied to para-legals: leĝa asistanto.