Welcome to the forum and Buen Camino!
If you want to see what other forum members are starting around the same time and add your name to the list of those starting in May click
here.
The first two weeks of May are some of the busy for those starting from SJPdP, so I recommend that you book accommodation up through Pamplona. After that there are more intermediate towns and the pilgrim traffic tends to spread out. You can then "wing it" or make reservations a day or two ahead.
I haven't walked the Valcarlos route, but doing so won't avoid significant elevation gain if that is your concern. You will also have to be careful on the descent into Zubiri.