In standard applescript (without scripting additions), just like in Classic Mac OS, only the Finder can delete items - & only by moving them to the trash first & then emptying the trash. However, if you'll be replacing the deleted items with files/folders of the same name, you could skip the delete step & use "with replacing", which will replace items in the same folder with the same name as the items you're copying/moving, without asking for confirmation. For example:
tell application "Finder" to duplicate alias "MyDisk:MyFolder:MyFile" to desktop with replacing
Also, since in OS X the Unix "rm" command will do exactly what's needed here, a scripting addition such as
OS X Power Additions Lite that allows implementing Unix commands within applescript could be used. The command would be something like:
Shell "rm -f /Users/Username/Desktop/MyFile"
This would, however, require that the scripting addition be installed on the computers of all users, which may not be what you're looking for. That is, the scripting addition would be a system requirement for users running the script. In OS 9, it was possible (with appropriate permission) to "bind" scripting additions to a script using a third party utility, so that the user would only need the bound script. As far as I know, this functionality isn't yet available in OS X, but hopefully will arrive soon from third party developers.