I think you can. Sure, some (ok, pretty much all) skills are better with perks and you don't have enough perks to do everything. But it depends on what you want to do.

1h and shield. No problem. You don't need to take every perk. 5 ranks of each of the 1st perk would serve well I think.
Sneak. No problem. Perks help, but you can probably get by with the first perk "Stealth" with a few ranks.
Magic. Depends on what you want to be. You can focus on destruction and pick the perks to lower magicka cost plus the augment.
Light Armor: No problem. pick Agile defender ranks for protection.

Listed above might take 20-25 perks out of 50. More if you pick up other magic schools. Maybe a few in archery or the sneak archery damage perk and possible leveling smithing a bit to upgrade armor and weapons with the "twice as much" bonus perks. But you don't have to go overboard with it.

Every situation is different and others are correct as you won't be as tough as a specialized character. And you probably won't make it on Master difficulty. But I think you can have a good time with a viable build. Heck, most of my mages have a pretty decent sneak skill and I don't have perks.

If you do pick up some of the later perks (like sneak's 15X dagger damage perk) you might end up using only that style as it becomes very effective. Hence why so many people specialize.

I have a PC at level 80, that I've specialised in trees from all classes. I don't thinks there has ever been simplistic class specialisations in TES such as warrior, mage and thief or stealth class. If you have a look at the specialisation available in Oblivion and base your character building on one of those classes, you'll probably get close to what you are trying to achieve.

I'd say being a combination/hybrid of sorts is variety. For example on my Lets Play or adventures of Skyrim on youtube I'm technically a Thief, Mage and Warrior all at the same time. Building sneak is incredible easy too so that's maxed out to 100.

Personally i'd recommend play the style you feel like it, I haven't had any issues being level 43 against any enemies and I doubt i'll be maxing out my character to 81 at all.

The one thing I am disappointed about is how difficult or annoying it is to build up speech to get the investor perk. by the time you get that you won't even need it.

Specialize in the Sneak perk-tree for your thieving side (other thief trees are somewhat redundant)
Go One-Handed and Shield perk-tree, as well as any type of armor you want for your warrior side
Pick whatever magical skills suit you, alternating them with your shield whenever you need to. This is how I play and I do pretty well (although I don't use perks on my current playthrough)

There is a glitch in the Black-Briar Meadery when talking to the Bosmer at the counter; simply keep persuading him to tell you about how Maven really is and it will get your speech up. A cheap way, but the only way to level it up before speech becomes redundant in trading

Playing a "red mage" style of character that's a little more spread out than a pure battlemage. On the expert difficulty, even with enchanting and smithing superior gear I get my arsch kicked left and right. Facing dual wielders often ends in death if I don't come at them right. But the difficulty is so very fun.

You can play as whatever you wish, so yes. All you have to do is play the elements that you want your character to have.