If you can add custom code you could create an event receiver feature for the list item ItemUpdating
event for the wiki in order to check for the presence of a web part and cancel the save and display a message.
Event receivers for lists will fire for all lists based on a template (so in your case all wiki libraries) if you only want this to operate on an individual instance then modify the sample code below to check for the wiki library instance you want to control.
public override void ItemUpdating(SPItemEventProperties properties)
{
base.ItemUpdating(properties);
SPListItem item = properties.ListItem; //get the list item being updated
string pageUrl = item.Url; //get the item url for the web part manager
SPLimitedWebPartManager lwpm = properties.Web.GetLimitedWebPartManager(pageUrl, PersonalizationScope.Shared); //get the web part manager
if (lwpm.WebParts.Count > 0) //test for the presence of any web parts
{
properties.Cancel = true; //cancel the save
properties.ErrorMessage = "WebParts are not allowed on this wiki page."; //display message to the user
}
}