Monitor switches: is this possible?

We have ordered 3 new Cisco 2950's, and we want to monitor them with SNMP.

Our external network (a /27) has been split into 2 /28's, with 1 dedicated for the webservers (behind a loadbalancer). We also have an internal-only network (see schema below).

Would it be possible to attach Switch 2 & 3 (latter one only is for internal network) DIRECTLY to switch 1, give them an IP-address within external 1 -ip-range, and thus access them remotely ?

Or would we have to setup tunnels/forwardings to access 2 & 3?

Pier

Code: 
                           |       
        ------ Switch 1 -------------         External 1
                            |
                          BigIP
                            |        
                  ------ Switch 2 -------     External 2 (loadbalanced webservers)
        
        ------ Switch 3 -------                Internal (10.x.x.x)

 

 

 

 

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