First of all,
Please make sure you are using the latest "stable" version, which is Virtuemart 2.0.18a for now.
I don't know what has changed with VM2.0.18c, our VM Template supports only stable versions.
Probably the upcoming stable version will be VM2.0.20 so until that, don't upgrade to any newer VM versions.
About the download link, i just resent you a new download ID to your email, and YES you can just take the /mod_virtuemart_search folder and upgrade the module only, that's fair. Since updating is all about copy-pasting files, basically you can leave the old files and upgrade only the files/folders you want by taking them from the Installation ZIP and paste to your website.
What was your current version of PureMart? For instance, i assume you did some changes in flexibleVM2Global.css
So never overwrite that CSS file while upgrading PureMArt, otherwise you will lose your CSS modifications, and everything will be back to stock.
Regards.
Forum Support.