At .001 seconds per query (might be less), that would be 100 seconds/month, and would be a gnat on the overall server load. Anyway the proposed 1/min cron job runs 43200 times/ month, whether it's needed or not.
I think one might then also consider doing the delete only on the main page upon entry, for example? which in your case would be at the very least 2/3 the cronjob load.
On the other hand, on a site that busy the php scripter would likely be somewhat beyond the point of saying 'gosh, how do I do a cron job??' or 'can I set up a cron job per record??'
The cron job adds multiple points of failure in a project driven by a novice. Sometimes stupid and simple is OK, even if not the best or most elegant answer.