Is there a source for statistics of deaths by wildlife in Africa? I've looked around and only find anecdotal or sparse information that doesn't really give a continent-wide view.

Unfortunately not. Most African wildlife departments are still stuck in the pre-digital era, and few deaths even make it onto paper.

What's interesting to me is how differently people react to say, an elephant or a hippo (chance of it killing you moderately low), compared to how they react about road risks (chance of being killed, very high). I think we're evolutionarily programmed to take note of wildlife, not cars etc.

Interesting question but no good data. I tried to track down some numbers a few years ago for a book. Mostly underestimates but here are some rough numbers
Africa: p.a
Malaria was 1.2 m, now about 800k
TB about 1.2 m infected
HIV about 25% of Soutern Africa pop
Sleeping sickness about 300k
MVA South Africa about 40k deaths , similar to USA 34k
Murder SA was 100k now better? At 50k but about 340k since 1994
USA deer 30, cattle 30, bears 10-20
Snakes 100k (National Geographic, mostly desert viper?) but more likely 50k
Crocodile 1000-3000k
Hippo 200
Lion 100-200, were 100-120 pa in Kruger Park with illegal immigrants
Elephant ~20
Leopard. Most frequent injury in Zim but rare deaths
Over 10 years hyena killed 45 in Zim. Don Heath
Rhino rare
Buffalo uncommon. Hunters
Sharks 30 world wide

Hence Terrible Twelve killers of Africa
1.humans
2.disease and bugs
3snakes
4sharks
5hyenas
6 crocs
7hippo
And big 5
Black rhino
Ele
Lion
Leopard
Buff

Nat Geo is usually pretty accurate,
but I would query the snakebite stats. I think way over.

And as has been said, African epidemiology is in the dark ages in most countries, so most human:animal conflicts would be under-reported.

Is a mosquito considered "wildlife"?

Opus, Apart from Bill Gates releasing some tame ones at a TED talk the proportional tame population is endangered