No. Do not wake your baby in the morning.
This sounds like a pretty crazy schedule for a baby to me. I'd start gradually moving bed time earlier (slowly). Latest bed time should be at this age is probably 7:30, maybe 8.
If you are still doing 2 naps, I'd shoot for a 2-3-4 schedule. So, if baby wakes at 7, first nap will be at 9. Second nap is 3 hours after the end of the first and bed time is 4 hours after the end of the second nap. It would look something like this:
7:00 - wakeup
9:00-11:00 - nap
2:00-3:30 - nap
7:30 - bed
Smilelari, you always have excellent advice, but I have found that you promote more sleep than my DS ever needed. I had it stuck in my head that DS needed hours upon hours of napping in a day, and so naptimes were a battle. In reality, he does NOT need two naps of two hours each and he definitely doesn't want them. For us, limiting daytime napping has created a better bedtime routing and more solid nighttime sleepling.
There you go. Do what works for you, of course.
We battled sleep a lot with DS. He didn't STTN for a long time and woke earlier and earlier and earlier. In the end, it turned out to be that we were underestimating his sleep needs. Moved his bedtime earlier and took naps more seriously, and poof! the problems disappeared. I take most of the general sleep advice from Weisbluth. Followed Weisbluth's guidance from the beginning with DD, and we've never had any serious sleep issues.
I'm sure needs vary a little from kid to kid (although Weisbluth claims that the variations are much smaller than most people think), but every time I hear about horrible toddler tantrums, I have to think that the reason DS is so easy going is because he's well rested. We had a stage at around 2.5 where he was refusing naps and people kept telling me that he was ready to give them up. We muscled through and he's back to sleeping 11-ish hours of sleep at night and 2-3 hours during most days. We don't really have any major tantrums unless we skimp on sleep.
Honestly, we have bigger nap battles when our kids are getting too little sleep than when they are on a routine and getting enough. When I try to put DD down at 7:15 p.m. and she fights me, my first guess is always that it's because she's overtired
DD isn't actually getting the amount of sleep above either, but she's also transitioned to 1 nap. Nap consolidation tends to cut things back a bit.