The short answer is "no".
Cached credentials are maintained in special Registry keys. These keys are only accessible by the SYSTEM account. In order to impersonate the SYSTEM account, you must have Administrator access to the system.
You might be able to write a script or something that can bypass #1. However, in the absence of any flaw in the OS (which cannot be reliably presumed, since it would likely be patched at some point), you cannot likely avoid #2. And, since the cached credentials are stored in the Registry, #3 is non-optional no matter how you want to do it.
I believe you can get away without using the SYSTEM account, by modifying the configuration options that define how the system handles cached credentials instead of messing with the cache itself. However, this will still violate your #2 & #3 requirements because the options are stored in the Registry and do require Administrator permissions to modify. Additionally, it may require one or two re-logins or reboots to be effective.
Sidenote: This question, as currently written, is perhaps more appropriate for Server Fault or Stack Overflow. Nevertheless, the answer remains the same.
EDIT: For more information about where the cached credentials are stored and how to modify settings which affect them, you may want to check out my related question on ServerFault.