Look for logic level MOSFETs if you want to use them. Either way, you are assuming an open-collector (or Open-drain) circuit. If that is the case, great! If not, then you'll need to revisit your plans.
A transistor should work just fine. The only one I recognize off the top of my head is the 2n3904, and it should suffice for what you want. Just remember that while a MOSFET is voltage driven, a transistor is current driven, so you need the appropriate resistor in series with the base to supply the correct base current.
I am also assuming you will be using an open collector circuit.
Dawiinci: So my transistors wouldn't work?
I am not sure about the circuit. The buttons simply shortcut GND to the board. Therefore I assumed to do this with a transistor.
They might work! What you need to check is how the rest of the circuit connects to the button. Most likely you will be able to replace it with a transistor. I'd recommend the standard 2n3904 or 2n7000, though the BS170 should work as well. Make sure you have it hooked up right.
The C945 (2SC945) that you have is a nice choice as it is a very high gain (Beta) GP NPN Silicon transistor... Any of them are more than suitable but you already have the C945 transistor..
First you need to find out the max current draw of your remote - then decide on a transistor, since it needs to be able to handle that current level. If the current draw is small it will make the choice easier of course.