I'm assuming you're in the US.
Get a tester and see if the box is grounded. A two lead neon type tester works well for this. Insert one lead into one side of the two-prong outlet and touch the other lead to the screw that holds the plate on. Try the other side, too. You may have to scratch off some paint if the screw isn't bare metal. If it lights up that's good news. You can use a multi-meter set to read AC voltage or another type of tester instead of the neon one.
If you have grounded boxes, you can either buy two-prong to three prong adapters that have a lug that you put the plate's screw through or you can buy replacement outlets that are designed for retrofitting in this application.
Your other option is to have an electrician come in and upgrade your wiring to full grounding.
Call me old school, but I am not a fan of some of the new friction grabbing splice devices out there. Similar spring connectors have been used on spec grade outlets for many years for 14awg copper. I have seen many failures and intermittent connection problems with these push springs. My theory, and just a theory mind you, is that there is not enough actual contact surface between the wire and the connection device and that the contact tension cannot be tightened. Over time expansion and contraction of the wire, surface tarnishing and dust can compromise the integrity of the connection. This happens with copper and much more with aluminum. As the surface area of the connection shrinks from any of those factors, heat and arcing can be created in the connection. Eventually failure can result. If you look at the comparison with a good wire nut or screw fastening terminal strip, you will see that there is much more metal to metal contact, the conductors can be twisted together and the tension can be tightened at any time with a twist or a turn of a screwdriver.
An other concern I have is the use of these type of connectors with aluminium wire. I have had nothing but bad experience with alu branch feeder wiring over the years. You must be absolutely sure the device is Al/Cu rated at minimum and that connections are as tight as possible. On larger wires such as service entries where alu wire is still used regularly, a substance known as NOLOX is always used on these connection to fight corrosion and assure good conductivity between the wire and landing connector. I also use NOLOX on any dryer or range connections that have alu wire. Alu wire tarnishes very quickly and expands and contracts faster and more than copper, therefore needs to be secured firmly and protected from corrosion wherever possible.
The last reason I am not a fan of friction fit connectors is that they can be miserable to work with after initial installation. Yes, they are fast easy to install the first time, but if you need to modify a connection or trouble shoot a problem where these connectors are installed, it is pain if not impossible to remove wires temporally. Reinserting a wire often doesn't have the same grip as before.
I may be all wet on this one, but I'm not ready to give up my trusty high quality wire nuts and screwdriver yet.
Best Answer
Those shaver sockets are actually a small transformer with 1:1 windings. That provides mains voltage in, and the same voltage out. The only difference is the output voltage is "fully floating" with absolutely no ground return or reference. You could accidentally touch the voltage and the faucet with no current flow. The only way to get a shock would be to touch both sides of the output.