If you really don't want your old catalog and the way it is set up, then you can choose not to have it upgraded. But remember that all of the work you have done on the images in Lightroom 4 will be lost as far as Lightroom 6 is concerned. You will be able to import those images again, but none of the adjustments will be there. It will be as if you have imported new images, and you will have to start all over again. If that is what you want, then don't upgrade your catalog. You can do the upgrade and rearrange things. And you can even start a new catalog if you want after you have upgraded the old one.
Jim is right here. There is another possible option to have at least the edits and ratings saved though. This method won't save Flags or Collections though.. and no virtual copies will come across.
First open the Lightroom 4 catalog in Lightroom 4. Over in the Left Panel, open the Catalog panel and choose All Photographs. Make sure Filters are off.
Now select all using Control + A (PC) or Command + A (Mac), then use Control + S (PC) or Command + S (Mac) to save metadata to the files. Let this run completely.
Now in Lightroom 6, just import the files you want in there, and the edits will come in with the files.
Other options while in the LR4 catalog: Filter to find flags and apply a color label, which will be saved to metadata. Filter for Virtual Copies and go make Snapshots of the file in Develop. This saves to the master file, so you can access the settings again.
This is only a suggestion, but may help if you really want to start organizing a fresh catalog in Lightroom 6.