Do not disconnect any wires without first labeling them so that you could put everything back the way it was if somebody told you to. Do not discard any parts until after you have everything new installed and working.
If you cannot find a double switch (with two toggles or handles) with one side one way and the other side two way then get a double switch both sides of which are two way. A two way switch (called 3 way or single pole single throw in the U.S.) can be wired up as one way (called on-off or single pole single throw in the U.S.), it just costs a little more money to buy.
To use a two way switch as one way you connect one of the wires to the common terminal and the other wire to one of the traveler terminals.
If you cannot find a double switch (with two toggles or handles) with one side one way and the other side two way then get a double switch both sides of which are two way. A two way switch (called 3 way or single pole single throw in the U.S.) can be wired up as one way (called on-off or single pole single throw in the U.S.), it just costs a little more money to buy.
To use a two way switch as one way you connect one of the wires to the common terminal and the other wire to one of the traveler terminals.