If it's 802,1D then down time can be up to 50 secs as Spanning Tree reconverges. But instead of lowering the cores and taking them down, why not raise the priority of the switch that you want to "remove"?
switch(config)#spanning-tree vlan x priority 61440
The priority values you can use start at 0 (zero) and go up to 61440 in increments of 4096, so 0, 4096, 8192, 12238, etc, with the default 32768 being the mid point.). Low numbers are the winners in Spanning-Tree elections / convergence situations so setting a switch to prioroty 61440 means it will never win the Spanning-Tree Root Bridge election, but the election / reconvergence will still happen. Altering priorities gives you a predictable, if slow, result.
BUT, whilst you are scheduling down time, why not convert ALL your switches to Rapid Spanning Tree (RSTP, IEEE 802.1W), and add in some extra redundant links and configure an Etherchannel.
To "switch on" Rapid Spaning-Tree, the command is:
switch(config)#spanning-tree mode rapid-pvst
This command affects all VLAN's and it's *MUCH* better. With RSTP running on all switches, convergence at layer two on a small-ish segment is almost instantaneous. BUT, if a single switch is left to run ordinary Spanning-Tree, full convergence takes up to 50 seconds, so make sure you change them ALL to RSTP.
It's *extremely* rare for me to come across a network running ordinary 802.1D Spanning-Tree because of the slow convergence time, and at the Core Layer, none of my networks rely on Layer 2 convergence as there are routers at the core, they are mostly Layer 3 switches (as well as the aforementioned routers) so we use EIGRP and / or OSPF for faster convergence across all devices at the core.
