LACs don’t just offer “arts” (as in"arts&letters") they offer everything except professional subjects such as Nursingor Engineering, but are undergraduate-focused and thus more flexible. They would have Math, Physics, CS, Chemistry, Biology, Cognitive Science/neuroscience, Environmental science, etc.
You’re typically admitted to the whole LAC and aren’t pigeonholed into any major or department, you can add a major or minor as your academic interests develop.
But everything has an exception 
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Flexible universities are Case Western and URochester, and Lafayette or Trinity CT offer Engineering. Or you may even enjoy Brandeis’ new approach (now, Saudi Arabia → Brandeis would be unusual but they have a mix of religions and the college isn’t religious.)
Premed pre-reqs include 5 high octane chemistry classes vs. 2 biology classes. Chemistry, especially organic chemistry, is THE weed out subject.
Engineering is mostly Math&Physics, with some chemistry thrown in, plus biology in some cases. Based on what you said, you want a curriculum where you have hands-on applications right off the bat.
It’s fine to “do math&deal” even if you don’t like it but hopefully your curriculum would include subjects you like, such as writing. Engineering in the US is the least flexible option, with little leeway for minors compared to other subjects&majors