Empire of Shadows by Jacquelyn Benson

Nice Victorian ladies don't run off to find legendary lost cities.
One trifling little arrest shouldn't have cost Ellie Mallory her job, but it's only the latest in a line of injustices facing any educated woman with archaeological ambitions.
When Ellie stumbles across the map to a mysterious ancient city, she knows she's holding her chance to revolutionize Pre-Colombian history. There's just one teensy complication. A ruthless villain wants it, and Ellie is all that stands in his way.
To race him to the ruins-and avoid being violently disposed of-she needs the help of maverick surveyor Adam Bates, a snake-wrangling rogue who can't seem to keep his dratted shirt on.
But there's more than Ellie's scholarly reputation (and life) on the line. Her enemies aren't just looters. They're after an arcane secret rumored to lie in the heart of the ruins, a mythical artifact with a power that could shake the world.
Between stealing trousers, plummeting over waterfalls, and trying not to fall in love with her machete-wielding partner, will Ellie be able to stop the oracle of a lost empire from falling into the wrong hands?
Empire of Shadows is the first book in the Raiders of the Arcana series, rip-roaring historical fantasy adventures perfect for fans of Romancing the Stone and The Mummy.
"Sassy banter and sizzling romantic tension sparkle throughout the fast-paced action ... Fans of Indiana Jones-style historical fantasies will be eager for the next adventure." - Booklist of the American Library Association
"A feminist, anti-colonialist tour-de-force, a pulse-pounding adventure tale, and a compelling, spirited romance all in one." - Charlotte English, author of the House of Werth series
"A page-turning historical fantasy romp ... Adam Bates somehow becomes more attractive with every extra layer of dirt." - Olivia Atwater, author of Half a Soul