The connector that the cheapino uses (8P8C) has eight pins while the 4P4C connector that I use has four pins. The cheapino uses eight wires to connect its halfs. So no, you cannot just use the 4P4C connector instead of the 8P8C connector.
Note that the terms RJ11 and RJ45 only specify the type of connector but don't how much pins it has. Use the terms 4P4C and 8P8C instead.
Thanks for the explanation! Yeah, I misremembered what I read about the cheapino not using all of its 8P8C wires (it uses 7 out of 8), but that makes sense.