There probably is some voltage across / current through the switch when it is activated even if you cannot measure it or see it. The switch will either pull a controller pin to 0V, to some voltage, or could be a cross-point switch on a keypad matrix.
A relay is the easiest option because you don't have to care what is being done inside the toy, you simply fake the physical button closure.
You can fake a closure other ways but one should analyse the circuit in the toy to decide what the most appropriate way is, and that may differ from toy to toy. If not using an appropriate means of switching that may be damaging or reducing the life expectancy of the toy.
If not worried about damage or life expectancy you can simply try things and and see what works. I have a digital picture frame that appears to use a matrix keypad scanning mechanism but shorting a switch input to 0V via a resistor activates the associated function. I simply wire the switches via resistors to PICAXE outputs and have them set as INPUT then LOW when I want to fake a button push. My PICAXE 0V is connected to the DPF 0V. I have no idea if that's causing any damage but I don't particularly care if it does.