The way I do it for CoD 1 with porting from CoD4/5+ is I use Lemon/Lime or either XmodelUtils/Xanim Extractor then in Maya fix them and I never used the CoD2/4/5 converter but there was none for CoD1 so I'm doing it in Maya. So open the rigged model then try to drag 'n drop the .tanim ontop of it and see how well it loaded and see what you can do about it. (Also a previous version of the plugin tools broke animations iirc, so perhaps update it?) When you drag 'n drop multiple .tanims after eachother your animation might become buggy, so it's best to reload your base model / .ma/.mb file.
Some examples which I think turned out quite okay.
ignore text
http://cod1.eu/webm/deagle.webm
the distance of the gun perhaps
http://cod1.eu/webm/ak47.webm
the first one is reload is bit off
http://cod1.eu/webm/raygun.webm