Your switch supports VLANs, so you should easily be able to accompish what your trying to do by simply setting them up properly. You'll want to put your router on 192.168.1.1 in the default VLAN(or wherever you want it to be). Then create two new VLAN, (3)192.168.3.0/24 and (4)192.168.4.0/24.
Once you've done this, you'll need to "tag" the ports and place them into the desired VLAN for that device. After you've done this, you'll need to setup a route within the Cisco switch so the two segments can communicate with each other. All of this is available on your switch per this doc, as well as instructions on how to actually do it:
Don't forget to setup DHCP within the switch, unless you like manually assigning IP addresses. Also, make sure the default gate of DCHP points to the switch. It can appear a bit hariy at first, but it's not difficult once you grasp the concept.
EDIT There will be a disruption is service when you initally add move the ports to a new VLAN. I would recommend setting up your routes first if possible to reduce downtime. If you do this, it should be less than 5 minutes.
This only happens the first time you add a port to a non-default VLAN. The best practice for this is to tag all ports to a high number VLAN the first time you turn it on(say 4000). By doing this, you can then freely change VLANs without causing a disruption in the future. This is especially important on trunk lines between switches.