Stabilizing

So I am bottling my 5 gallons of Ed Wort's wonderful brew today, and I need to stabilize it so the bottles don't blow up on me.

I bought some Campden tablets from the shop, as well as some stuff labeled "Stabilizer", which is white stuff that is not really a powder, but looks more like the sprinkles you put on ice cream (only white).

What am I doing here? I need to bottle today, so can I even use these? I just don't want the corks to blow off on me.

Edit: The wine has been fermenting for over 4 weeks, at about 60 degrees average.

is it crystal clear? like can you read a newspaper through the carboy?

4 weeks is like half the time most of us here like to let Apfelwien ride before bottling. Most of us go 8 or so.

if I were you - i'd let it be for a while (unless you are trying to precisely kill fermentation and hold a certain FG that you have reached)
but my experiance with Montrachet is it's already reached attenuation at week 4... it just needs to clarify.
only if you intend to backsweeten with a fermentable should you concern yourself with stabilizing your Apfelwien, if this is your intent - then ignore the following if you intend to bottle it still and dry... please read on

with the right kind of bottle, and smart brewing techniques you shouldn't need to worry about your brew "blowing up" without stabilizers. I never use stabilizers - however I bottle carb most of my apfelwien - (which in case you didn't know - cannot be done if you stabilize.) once your apfelwien is fermented to dryness, and clarified - unless you add additional fermentables there is no way to build pressure up in the bottles, as all the Co2 in the wine outgasses during the clarifying stage (week 3-4 to week 8-9)
if you follow good sanitation practices you really shouldn't need to worry about infection either - so no need to use stabilizers to counter that.

I've got a batch of 5 month old mixed berry country wine I bottled still in standard wine bottles in my collection, it's quite tasty - and was bottled unstabilized - I've had no explosions, or infections.

but the fact still remains - you'll be happier with the end product both in taste and appearance if you wait a bit longer before bottling - trust me, I'm pretty sure every brewer of Apfelwien jumped the gun on thier first batch when starting out and bottled early out of impatience - which leads experienced Apfelwien brewers to advise new Apfelwien brewers to let it be for more than 1 month... now if you must bottle today, it won't be "bad" (in fact it'll be pretty good) but for the price of another month... it'll be even better.
RDWHAHB