According to the Czech bibliography (An Annotated Bibliography of African Big Game Hunting Books, 1785-1950) the first edition of Wild Beasts and Their Ways. Reminiscences of Europe, Asia, Africa, and America was published in London by Macmillan and Company in two volumes.(8vo, brick red cloth with gilt spine titles, with gilt tigers and buffalo vignettes on the boards.) The second edition was a single volume published in 1891 and is "far more commonly encountered". So, I think the first question would be: do you have the a 1st or 2nd edition published by Macmillan in London?

There's a lot of dross on abebooks.com - for a book like this, there will be numerous print-on-demand reproductions and books claimed to be first editions that aren't, leather bound books printed in India... Here's a few listings with seller-supplied photos:

Some apparent real 1st editions:
About $270 delivered from the UK

About $300 delivered from the UK

Some apparent second editions:
$165 delivered from the UK

$56 delivered from New Jersey

Regarding booksellers, besides those mentioned above, two others that come to mind are:
World Wide Hunting Books is affiliated with Safari Press. They have a first edition for $850.

Coch-y-Bonddu Books in Wales.

I'm not sure what the best avenue is for selling off old collectible books. I don't have any first-hand experience trying to sell to dealers, but I expect they'll only pay a small fraction of the price they hope to sell for. I suppose it depends how many you have. I have several thousand books on hunting and fishing and think from time to time about how I'll unload them. Haven't reached a conclusion yet.

As to whether or not anyone collects 130-year old Africana - yes, I'm sure there are, but I'm not sure what the market looks like now. Condition is very important; photos would help sell books. For me, the biggest problem buying on, for example, eBay is that there are often sellers who have no idea what they're selling; have no idea that there are standard definitions for book quality; and, package books in a way that might be OK for a $10 novel, but not for a limited edition book that might cost $75-$100. Lately, even reasonably well-packed books have arrived damaged. All these risks tend to hold prices down, or at least what I'm willing to pay.

Good luck finding a buyer!