While China certainly is Non-Schengen, CPH definitely is Schengen. So you're locking at immigration in VIE (and security as well, since TPE isn't "clean") as in a Non-Schengen to Schengen connection.

On separate tickets, I'd not do that with less than 2 hours connection time (no luggage, boarding pass in hand), or 3 hours (luggage, need to retrieve boarding pass) - and even more during busy times (holidays) since booking a ticket on the spot might not be even possible then. Or rather expensive. Since we're talking short-haul. The other way, ie short haul connecting to long haul on two tickets, I'd give myself even more time - much more problems in case of a missed connection.

The low MCT's in VIE really only works connections on one ticket, and preferable both flights on OS (or at least LH group) - they'll hold flights, especially long hauls. But if they don't even know you're coming, the gate most probably will be closed once boarding is complete. Why wait for a passenger if it's not their problem? And on two tickets, it won't be their problem at all..