It looks good. I have only gone to Wakayama using public transportation (train and bus), so I only know the time it takes between these locations by these.
Osaka to Shirahama is about three hours, you should get there in the morning. There is plenty to do there. Beaches... Sea Caves... Museums... Energy Land and Adventure... World... and Public Beach Onsens (bathing suits requires). An afternoon here might not be enough time.
http://www.japan-guide.com/e/e4958.htmlShirahama to Kii-Katsuura should be an hour and a half drive, giving you plenty of time to visit Nachi Falls and Nachi Taisha. If you feel like a hike, you might try the Daimonzaka portion of the Kumano trail near Nachi falls. It is 2.2 Kilometers long, and concidered an easy hike. You should be able to get a shuttle bus to the trail head, and walk down.
http://www.mustlovejapan.com/subject/kumano_daimonzaka/spot1208.htmlI like the Hotel Urashima in Kii-Katsuura and it's sea cave Onsens (two or the six baths). I would also suggest asking when the Sushi chef will be doing a tuna carving demonstration at the buffet, if you go this route. Here is a nice blog with photos of the hotel:
http://natalysunsmile.blogspot.com/2013/08/hotel-urashima-resort-spa-w...The bus ride from Kii-Katsuura to Hongu was very beautiful. It takes about two hours. The drive follows a river up a valley, and for most of the journey, it was without towns. Houngu-Taisha was nice, and I would recommend walking part of the Kumano Kodo trail before going to your Onsen.
I have not been on the drive from Hongu Taisha to Mount Koya. There are three route for public transport, and my guess is that you will follow the Purple path suggested at the following website.
http://www.tb-kumano.jp/en/transport/hongu-koyasan-access/It's going to be a long day of driving, and of the three paths, this is the longest (six hours). The other two paths are only a half hour shorter. These times are by public transportation, so you may be faster than this. If you take the yellow path, you would go close to Yoshino, which is best during cherry blossum time.
http://www.japan-guide.com/e/e4150.html Either way, considering the public transport is 5.5 to 6 hours, I would not try to then go to Wakayama after visiting Mount Koya. I would recommend doing a temple stay.
If you have already got the Wakayama hotel reservations, I would just go directly there, and on the following day, go to mount Koya before returning to Osaka.
I hope this helps.
