One possibility is to move the call to user_function() outside of the KeyError exception handler so that user exceptions won't be chained:

def wrapper(*args, **kwds):
    nonlocal hits, misses
    key = args
    if kwds:
        key += kwd_mark + tuple(sorted(kwds.items()))
    try:
        with lock:
            result = cache[key]
            cache_renew(key)        # record recent use of this key
            hits += 1
            return result
    except KeyError:
        pass
    result = user_function(*args, **kwds)
    with lock:
        cache[key] = result     # record recent use of this key
        misses += 1
        if len(cache) > maxsize:
            cache_popitem(0)    # purge least recently used cache entry
    return result