Image was just for reference. I would not use a 2n3906 as well but a BC547 (the standard NPN in Europe) but any little NPN will do as the current is low. But yeay, we have no idea what "the other IC" is or what it will draw. 1k ill be fine but 10k will work just as fine as the current is low.
You need PNP transistor if you're switching the high side, not an NPN transistor.
Is there a possibility that the chip will be receiving 5v inputs when not powered? If so, depending on the details of the chip and rest of the circuit, that could damage the chip.
Thank you for answering my question. If I understand correctly you are trying NOT to run two external ( to Arduino) processors (I/O?) , not just IC chip, in parallel. ( Do you have common I/O lines in parallel connected to to each processor ?) Not knowing the details of your setup it still seem as very crude and potentially unreliable solution.
I hope you are aware that any processor goes thru power up / power down process in preset time so you cannot expect to be able to switch them "on the fly".
Good luck with your project.