Since you don't have shell access, you'll have to find an FTP client that will do the chmod command. I know that WS_FTP does. (I use the free version, it works fine.)
I don't know of any FTP clients that will do the chown command, which means that in order to let apache write to the file, you'll have to let anybody write to the file.
Instead of a command line, in WS_FTP, right-click on your file and select the "chmod (UNIX)" option. Check off read, write, and execute for each of the three groups ("user" "group" and "other"). Please note that this is pretty insecure, and you DON'T want to do this on a production server or anything more important than a personal web page counter.
Lacey