You can find this old K-Meleon portable versions:
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 preferences, 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.
You can deleted setdefault.exe and loader.exe in your USB memory device K-Meleon folder because I don't think they would be needed on portable version.
You can download from here the modified file resulted: xpcom_core.dll
Note: This xpcom_core.dll file could not be upgraded to the latest version of K-Meleon.