that's really up to you, it'll take more time but you will probably save a bit of sP.
I swear I saw a post from staff saying that gold accounts would consider both old and new shops.
Oh I don't know, I haven't been following things too closely.
If you use the New Shop Search, you will get to see all the shops, both new and old. I've tested this by running duplicate searches (old and new) and it does seem to work.
However the link from the quest goes to the regular shop search since the new one isn't available in general yet. That means opening up the new search and copying item names in the old method. It would guarantee the lowest price, but take way longer.
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My tests match what said.
IMO it takes longer to search by pasting than your time playing sP quests is worth. You don't save all that much. I know as far as my newshops, I have only started to get around to pricing them as Autoprice isn't working on newshops, or perhaps because I never use it I just can't stand to sit around until it dopey derpy doh doh gets around to it.