You can hide a registrant's fundraising page so only admins and this member will be able to see this page and to hide the member from all searches.
You can achieve this by following these steps :
1) Go to admin panel -> People -> Registrant tab
2) Click/Dbl-click on the registrant you want to update. This will display a pop-up display.
3) Click Edit button on the pop-up to start making the changes.
4) Scroll down to "Is Fundraiser" section and check the "Hide Fundraising Page" checkbox.
5) Click on the Save button in the bottom of the pop-up to save the changes.