I probably shouldn't go into it to much in this forum, considering Mongoose isn't doing a SW game
But to answer your question - there's no need to do a Dodge trait in SW, its covered by the Parry trait. Parry would have been better titled 'Defence', covering both Dodge and Parry. But there's no need to tinker with the core dynamic, it's covered.
However you could make Dodge an Edge perhaps, if it isn't already listed (there may be a similar Edge that covers it, however). You may find that its already covered under a combat manuver as well, I'm a little rusty, but its possible its there. Many D20 Feats are covered in SW by combat manuevers that anyone can attempt, so don't overlook manuevers. One thing is not to mess with the SW core system, but to tinker around with Edges instead if you find something's not covered
As far as getting rid of the card based Initiative system, thats fair enough. The card initiative system is flavoursome for the western setting, but feels clumsy to me for other genres. We rolled D20 + Agility dice to determine Initiative order, highest first. It did the trick for us. Wild Edges using the 'royal' cards were covered by rolling 20 on the D20 - not all that accurate crossover for the system, but again it works for my troupe.
Perhaps you should go to the Pinnacle forums on the Pinnacle Homepage - heaps of great advice for SW, very similar set-up to these Mongoose forums.
For Hyboria I have used SW for the core rules, and bought the Mongoose Conan products for resource material as they have done the background very well. It turned out to be a great mix, and I hope you find this as well.
Best of luck with it all!!