You can't find such portable tool.
More precisely, it can be portable as "no installation required" but it can't be portable as "no administrator privileges required". Direct disk access requires administrator on Windows.
The only way to erase free space without administrator privileges is create a new file taking all empty space on the partiotion and fill it by zeroes. But it doesn't satisfy you because of slowness point.
And a bit about software. I would've try Recuva.
- I've never used it for erasing, but it has such feature.
I used recovery there and it works great, so I expect erasing to be good too.
- It has a setting for keeping all the setting in ini-file, so it can be considered as portable.
You have to install it somewhere, switch to keeping setting in ini-file and just copy the folder.
- Anyway, you still need administrator privileges to run it.