I would prefer that people use the application rather than the web map because the application has more features and it allows me to put a disclaimer in the splash page.
Yes. You can share just the application and not the bare bones web map. You can just copy and paste the link (if it's public) or share it through other means. Some ideas are here:
Share maps—ArcGIS Online Help | ArcGIS
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What web application are you using?
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