For Chromium-based browsers, the way you apply policies is by forcing a registry key that matches the corresponding policy to the desired value.
Of particular importance to you would be the DefaultCookiesSetting and ForceEphemeralProfiles policy. You may find detailed instructions regarding the correct values to set and the required key to modify on their respective links. In this case, ForceEphemeralProfiles is the correct policy to apply, as clearing cache isn't a possibility by policy; only cookies may be cleared in such a way. Using ephemeral profiles, all profile data is persisted on disk only until the Chrome session ends.
If this is not an option (seeing as ephemeral mode will indeed wipe things like extensions too), you may deploy an extension like Auto History Wipe which exposes cookie and cache clear functionality on a granular level.
I hope this answer will solve your issue.