Vodafone and even ancient J-Phone 3G handsets will work just fine on the Softbank network.
The bigger question though is can you use a pre-paid SIM in a non-prepaid phone? I have no idea and have never tested it but I suspect that you might not be able to do this. In that case you would need to hunt down an older 3G prepaid handset, probably a lot tougher to do.
Why would you want to keep a prepaid phone though? Just buy a used phone and get it activated at Softbank on the 1000/yen a month White Plan. As you aren't buying a phone there should be no need for a 2 year contract and the cost per minute is FAR less than with prepaid.