You should have no real problems running it at 300 without a fan. I don't recommend it, but it probably will work.
Reason behind this madness:
I've run a PII 333 w/o fan for a year with no issues. This was with a generic coolermaster-like HSF with both fans broken.
My roommate has run a PII 333 for over a year with a tiny heatsink that allows for no circulation. (Designed for use only with a fan, but the fan was broken). No problems there either, though I thought he was crazy for doing it.
I OCed a PII 300a to 450 using the same heatsink that my roommate had. To ease my mind I put on the only fan I had: an old Sunon 40mm fan (~5cfm?). Then I ran RC5 all day. Max temp in a 77F room with a jammed case: 53C. I replaced this setup after a week, and the HS was hot to the touch, which is never good. Now runs at 40C using a coolermaster-like HSF with one fan.