Why is the IP address necessary? I guess you want it in order to send a "valid" ARP request that will generate a response. This is not necessary. The basic algorithm for recovering a keystream via frag attack is as follows:
1) Obtain the first ~8 bytes of keystream with the usual plain-text XOR cipher-text trick.
2) Send a packet using ~8 byte frags and capture relayed version from AP. XOR the cipher-text [relayed from AP] and clear-text [whatever you sent].
In order to do #2, you can send any packet that is a broadcast. The AP must, and will, relay any broadcast packets. Indeed, the packet need not be ARP. It can be a packet full of zeros. In that case, the relayed version will simply contain the keystream [it even saves you from having to XOR

]. Thus, it is not necessary to send a "valid" ARP request---any broadcast packet will do.
In short, I do not think that knowing the net's IP range is a requirement for the frag attack [for recovering a keystream, which is what it seems you are doing].