The 3560 appears to only have room for 1 image at a time . Is this true ? Why does cisco only have enough flash to hold 1 image . This makes it a higher risk job if you have to delete flash and hope the wan doesn't go down or the switch lose power while you are downloading the new file . Don't see files you can delete in flash:
8977408 bytes is not enough to download a newer image and have both in flash, newer images are over 9 meg in size.
Without sounding like a jerk, the 3560 is a low end device, there has to be a happy medium between cost and functionallity.
Now for the good part :) . . . and I am making a big assumption here. Setup another Cisco device on the local broadcast domain - that has enough space on the flash - as a TFTP server and copy your new image from that device to the 3560. Pick a device on the local b/c domain that does not care what type of data file it holds. If you don't have this type of device, you may have to enable a local tftp server (Windows PC).
If the 3560 switch looses connection to the wan, no problem. Also ensure you config the 3560 to recover from a failed flash upgrade to boot from the same local device as default - until the upgrade is complete.
To make your life easier, perform cleanup when you're done.
Thanks Edison , wow I must have read the file sizes wrong as I checked that version . Thats what I have been doing in places where there are multiple switches , 1 copy to a device then using that as a tftpserver. Now I just have to go back and check the 3750 file sizes and see if I can make 2 fit on one flash.
The new generation of switches, from 2350, 2960, 2975, 3560, 3750, have enough flash to hold a number of IOS from different switches. It all boils down to how you load it.
In your particular example, I'd delete the HTML subdirectory if you don't use it (use it or loose it, I'd say) and make sure you have a working BIN file to boot your appliance. Then you can put either a TAR or BIN file and use the appliance as a temporary TFTP file.
Another option is to use the local file server as a TFTP server. It takes about 5 minutes to setup using TFTP32.