AFAIK, the sites popularity is worked out on a sub of the hits, votes, and overall rating. Deleting one/all of these should stop links being popular... but you will loose your hits/rankings etc :(
Alternativly, you could just remove the "isPop" stuff in link.html, and then take out the section in Setup > Build Options > category_sort_order, so that isPop DESC is removed.
Cool sites are just built from the number of Hits - so one thing you could do if you didn't want to completely lose this information is just make another field in the links table called OldHits and copy the data from Hits into OldHits and then set Hits to zero.
Actually , i would never prefer to delete any "Data Gathered Over A Period Of Time". However, may be following could be added as a feature to Cool Links utility:
Monthly Span of Cool Links on the Cool page In Addition To The Global One which runs at present if possible. For example, one on the Cool page, Jan/Feb/Mar...../Dec sort of Monthly Stats for the Cool Links Be there, and Perhaps a similar stuff for "Top Rated" also.