Thank you all 
Again, i'm not an electronics guy (but rather software + musician), so please bear with me
(Btw: I already bought the mechanical relays, and according to the datasheet, they consume 150 mW.)
Anyway, I found this one: ULN2803 - 8 channel version of the ULN2003.
Seem to be the right size with 8 channels, but I'm just really unsure how to connect this.
I assume I feed 5v (from the external power supply) to the COM on the ULN - and then connect each arduino pin to the corresponding pin on the 2803? Would that do it?
Big thanks!