Safely hiding cables without a ground

I'd like to install some wall mounted speakers and hide the power supply as best as I can. I'm planning to install this product I found from Sanus in my recently renovated bathroom (which has 3 prong GFCI outlets): https://www.sanus.com/en_us/products/cable-management/wsiwp1/

However, my bedroom still has very old wiring with 2 prong ungrounded outlets. I know that this wiring should eventually be fully replaced, but it's not in my budget right now. I'm wondering if an in-wall solution like the Sanus product is especially dangerous in this situation. Since it's a 3 prong outlet I'd need to use an adapter to make it work. Is this a crazy idea? If so, what alternative would be recommended? Perhaps a corner-mounted raceway?

Any input much appreciated.