You can find this old K-Meleon portable versions:
Pocket K-Meleon 1.1.3 by JujuLand (based in old Pocket K-Meleon by Douglas McFadzean).
K-Meleon Portable 1.5.0 by Travis Carrico.
I don't think that a K-Meleon 1.5.x Portable version is needed.
You can convert standard K-Meleon 1.5.x in portable easilly.
In cache, uncheck "cache files on disk" option, and set "cache files in memory" to 20 or 30 MB, optional: you can uncheck also "cache website icons on disk" option.
In history, set "Keep a list of all pages visited..." option to 0 (zero) days.
Set others privacy options as cookies and remember login data as you like it.