I've been listening to this album since I was a kid but I've just realized that the Elvis Christmas album had one side of all non-religious songs and one side of all religious ones. 
 
Here are the non-religious ones.
 
Santa Claus is Back in Town (most rocking' Christmas song ever!)
White Christmas
Here Comes Santa Claus
I'll be Home for Christmas
Blue Christmas 
Santa Bring my Baby Back to Me.
 

Hmmm. Looks like you have a good list of suggestions. You have more than enough for a set. I'm not a christian ( although i was raised as one) but i don't find the songs dreary at all. Slower tempo does not necessarily equal dreary. It's not like the songs describe graphic depictions of crucifixion details :)  You may be overthinking it. I work with a lot of kids from non-christian backgrounds and most just care about whether they can get treats out of any of these holidays. We threw a community halloween event and most attendees were practicing recently immigrated muslims. Had never seen people in full muslim attire AND halloween costumes. In the end, they just liked the idea of free candy. 

How about the bob geldof one or the snoopy Christmas one. Or the pogues one. But please this Christmas lets keep it politically correct and don't say anything that may upset anyone else in anyway possible :) have a very politically correct Xmas everybody. E.g. Why does Santa Claus need to be a fat white man. Why not a smoking hot blonde with novelty size boobs? The kids can handle it, don't foist our prejudices etc upon them.

backwoods
 Why does Santa Claus need to be a fat white man.

Ask Coca-Cola, they invented him.

Scoot
It's also a lot more difficult to comprehend the ability of children with an average age of 5 1/2 and are just starting out with learning English.

Good point, avoid this song ! :)
 
https://www.youtube.com/watch?v=rFt1tAvnBvg

I have the Phil Spector Christmas album, it's a classic, and I never think of Religion when I play it.

Here is over 3 hrs. of Christmas Songs, pick 'em out yourself.
https://www.youtube.com/watch?v=jZ-e3_31sdM
 
 

ampfixer
I have the Phil Spector Christmas album, it's a classic, and I never think of Religion when I play it.

sadly, i don't think of jebus when I think of Phil either lol

How about: 
http://youtu.be/w9mXJ_KlQq8
 
DON'T HIT PLAY IF YOU FEEL LIKE YOU ARE SUSCEPTIBLE OF BEING OFFENDED.
 
The episode behind that song - a quest for a non-denominational Christmas symbol - is also strangely relevant in this context. :P

Rain
How about: 
http://youtu.be/w9mXJ_KlQq8
 
DON'T HIT PLAY IF YOU FEEL LIKE YOU ARE SUSCEPTIBLE OF BEING OFFENDED.
 
The episode behind that song - a quest for a non-denominational Christmas symbol - is also strangely relevant in this context. :P

It's seems a bit sh*t to me ;)