In a web-app you probably want the thread safety an atom provides, so it would be a good choice.
You can include a reference to your atom in your system config if you want to retain the reloaded-like / dependency injection pattern:
(def changing-config (atom {}))
;; system-map
(def sys-map
{:a "a"
:b 42
:c changing-config})
(defn my-handler
[handler sys-map]
(fn [req] {:status 200 :body @(:c sys-map)}))