Simple and safe solution to control a power plug with Arduino or PC
I would suggest two options.

First - and this involves a small amount of wiring and soldering - using a PowerSwitchTail II. This is a very safe way of switching mains voltage. There is adequate isolation, it is safely cased and tested.

If you really want to do no wiring or soldering at all, then I would suggest finding one of the common 434/868/915MHz (depending on region) remote controlled sockets using a basic OOK protocol, and buy a simple 434MHz transmitter. A number of the protocols are documented in various places. The only issue with these is that you have no sure way of knowing if the switch is on or off.