No, it is not clear that decriminalizing prostitution improves safety and public health, even though researchers have studied its simultaneous 2003 decriminalization in New Zealand and Rhode Island.
It's supposed by some researchers that "indoor prostitution" is safer for the prostitute than street prostitution (link) but other researchers oppose this claim (link).
It is not clear that the increased availability of "indoor prostitution" under decriminalization has any impact on street prostitution at all (link - see footnote). Unfortunately, the reduction in violence seen among all women in Rhode Island in 2003 was preceded by a rise in violence in 2001-2002, so the decriminalized state was still just as unsafe as its neighbors after the improvement.
Furthermore, it seems likely that decriminalization will enable other crimes against women, such as trafficking into the decriminalized area (link).
A 2014 study-of-studies determined that at a minimum, we observe that 3 in 10 prostitutes will become victims of violent crime. Some studies found that 3 in 4 prostitutes were victimized. (link) Nobody imagines that regulations will alleviate this insane risk, but merely that regulation could remove the black market's impenetrable firewall between perpetrators of violence and justice.
Also, decriminalized prostitution contracts will inevitably result in violence if a client changes his mind and refuses to pay, resulting in the poisonous legal quagmire of court proceedings to determine whether anything happened. If the court sides with the dishonest client, then it could become true that the prostitute had been raped.