Why not change the permissions? Permissions are there to use them. And this is a fine example of where group permissions are useful.
Try using a log directory with read+write permissions for your irssi user and read permissions for your web server user.
You could of course add an additional group for that purpose and put the web servers user into that group.
Example:
Folder /var/www/irclogs
Permissions:
User: [irssi-user] Group: [web server group] Mode (Folder): 0750 Mode (Files): 0640
That way your web server can read the files, irssi can read+write the files and no one else can access them(unless you set the mode to something else).