I used to fly long haul a lot (mainly for work) and I find with daytime flights, have a brief nap if you can (a glass or two of wine will help) and then power on through until your usual bedtime if at all possible. Once you're off the flight, just keep moving. Resist the temptation to have a snooze when you get to your hotel as that will mess your sleep up later.
I used to fly every few weeks to somewhere that's 10 hours flight from the U.K. and 6 hours behind. It's no big deal. Quite a nice flight length actually. Enough time for a movie or two, a nice meal, some reading and a reasonable nap. I'm not sure why people feel the need to change knickers and T-shirts when they're only flying for 10 hours. Maybe these people change their knickers halfway through the day at home as well?
I always take a small mist spray (Dermalogica) which I apply every hour or so, some eye cream (apply every few hours), some hand cream (apply every few hours) and a solid stick deodorant (keeps liquids to a minimum). And a travel size perfume (although careful how you use this as some people are very sensitive to perfume being used near them). I always carry lip balm wherever I am anyway so that's a given. I change into flight socks after take-off and slap some hand cream on my feet so they get nicely moisturised. I use the travel toothbrush and paste 1 hour before landing (before the toilets get too busy) and I take some toothpicks with me as well. I have a stash of Colgate Wisp Max Fresh at home and I bring enough to cover all my flights as these are great for freshening up your teeth just sitting at your seat.
I always take some Bose noise cancelling headphones (the small in-ear phones) plus some Flare Audio earplugs and a Masters of Mayfair eye mask. If it's a really long flight or overnight and I will need to sleep as I'll be going straight to the office on arrival, I take my own travel sized feather/down pillow with a silk pillowcase. I also have a really lovely huge pashmina that is silk on one side and pashmina wool on the other. Great to use as a light blanket or a wrap or just as a big scarf to dress my look up.
I drink lots of water but I also enjoy some wine as well.
I have light make-up in my bag. A travel size IT Cosmetics CC+ cream, some pressed powder, concealer and lip stick in case I need to smarten myself up before landing (or my luggage gets lost and I need to last a day or two with minimal make-up). I take a small hair comb and I sometimes take a travel size dry shampoo for very long flights but wouldn't bother for only 10 hours. I'd just use some dry shampoo before I left home as it helps my hair keep some body when sleeping on the plane and prevents any greasy roots appearing.