If I ordered nigiri sushi in Edo (Tokyo) in 1850, how much more of a health risk would it be compared to the same dish in 1990?

The three main health risks with sushi are bacteria, parasites, and heavy metal contamination.

We will begin with bacteria. My understanding is that the final processing of both rice and fish has changed little since 1850. The The Tale of Sushi: History and Regulations by Cindy Hsin-I Feng points out that "In the 1820s, Hanaya Yohei of Edo brought to Edoites a recipe variation most closely akin to the genre of sushi that modern sushi consumers are served today". This process makes use of vinegar rather than fermentation to preserve the fish. Side note: apparently this older fermentation process smelled not too good but still tasted yummy. The fish during the late 1800s, using vinegar, was likely more heavily salted than today so as to further help preserve it.

When discussing food-safety concerning fish it important to also consider modern flash freezing. This is important for preventing parasites (and I assume also reduces bacterial growth). However, flash freezing was not introduced until more recently (I am not sure when exactly it caught on in Japan, but it wasn't introduced until the 1929 in the western world). So, the risk of parasites in the food may have been greater in 1850 than in 1990.

The other major health risk is heavy metals, notably mercury. Biomagnification creates greater concentration of mercury in larger and older fish higher up on the food chain naturally, so it really depends which fish you eat. Modern industrialisation, such as mining and burning coal, also increased heavy metal contamination in fish so I would actually suspect a greater risk for that in 1990. However harm from mercury takes quite a while, usually many years of daily consumption, to occur.

All in all, sushi was not particularly risky in either period but there was a greater risk of parasites in 1850 and a greater risk of mercury ingestion in 1990.