MySQL MyISAM Table Locking and Delayed Inserts for Webserver Access Logs
FWIW, I think this is the wrong way to do this; unless you need to do real-time reporting on webserver access write the log as a file and bulk-load it.

Having said that, there is a way to do what you want, which if I understand it correctly is to queue up pending inserts while doing maintenance on your database. In other words, decoupling the webserver's INSERT operation from the actual INSERT in the database in some sort of buffer. The way to do it using two instances, one that is directly written to in which you will use the blackhole storage engine, and one that you will replicate to, which will be your "real" database. The pending inserts will live in the binlogs; you simply stop replicating to the slave, perform your maintenance, then resume replication again and the slave/real database catches up. The slave is available for SELECTs for your reporting. You can even multi-master for load balancing, or have multiple slaves and switch between them during maintenance activities.