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It will take some time for everything to change over in the search engines -- a possible major dip in traffic awaits. If you do this, give some thought about how you will handle requests for the old pages, and that means from any ser agent, spider or browser.
I don't know what resources Yahoo Stores have available for you. I would ask them directly before making any move. The best would be to 301 redirect the .asp requests to the parallel .html page (assuming every page can have its direct counterpart, of course.) Even doing this, I would still plan for a drop in SE traffic for at least few weeks (4 to 6 or so).
If you can't do this, then you have a real challenge. I would ask Yahoo about it -- they should have something to offer you. I can think of a couple approaches that might help a bit, but it will boil down to what their package can do.
All I would add is that the change of page names can happen very quickly these days!
I have move 90,000 page sites from .html to .php and it has taken less than a month to get all of the new .php pages indexed by Google, Yahoo and MSN.
Using redirects to minimize traffic loss is definately something you should do, but, the overall re-indexing process is now a lot faster than it was several years ago.
Also do you agree that html pages are better then the asp pages from monstercommerce stores?
Monster has an html catalog upgrade option. This creates html crawlable pages for the seach engines.
I would implement that, request the 'daily crawl" update, create sitemaps, and submit them.
I suggests this versus changing hosting and shopping carts. (and if you still needed to I definitely would choose Yahoo.
Gary