Yes you can :)
It's a bit tricky but each razor can modify what / how something is indexed, this is often needed when indexing List/Details-pages. Here's the starting point in the docs: https://github.com/2sic/2sxc/wiki/Razor-SexyContentWebPage.CustomizeSearch
I would try the following (haven't tried it myself, but should work)
@functions
{
/// <summary>
/// Populate the search - ensure that each entity has an own url/page
/// </summary>
/// <param name="searchInfos"></param>
/// <param name="moduleInfo"></param>
/// <param name="startDate"></param>
public override void CustomizeSearch(Dictionary<string, List<ToSic.SexyContent.Search.ISearchInfo>> searchInfos, DotNetNuke.Entities.Modules.ModuleInfo moduleInfo, DateTime startDate)
{
// clear the search-infos
searchInfos["Default"] = new List<ToSic.SexyContent.Search.ISearchInfo>();
}
}