I've seen some people accomplish this by configuring the two-node cluster and leaving one side down, in effect running with a failed node as normal operations. However, I suspect by not being "RAC-enabled" your application uses some sort of connection pooling at startup that may require a restart of the application anyway when failing over from one node to another.
Also, you are correct that 10g SE does not come with the Data Guard option, but you can manually simulate this by copying your archive logs to the standby destination and issuing a "recover automatic standby database" command to apply them. Besides having to script this and closely monitor the process, you will lose the graceful switchover flexibility and have to rebuild your standby database again after activation.
This was first published in October 2006