You can add chemicals to your skimmer, but it is not a best practice and not recommended at all. Even though your pool has no skimmer, adding chemicals directly to your pool provides an effective means of dispersing the chemicals in the water. However, it would be best if you made sure the pump is running.

What is Pool Stabilizer?
The chlorine level in your pool can easily be affected by sunlight, and the only way to reduce the effect of UV rays on your pool is by applying a stabilizer. Pool stabilizers are chemicals that are added to your pool to prevent chlorine from dissipating from your pool easily.

To avoid spending much money treating your pool, you need a very strong stabilizer that can be active for weeks. With this, you get to keep your water sanitized for a longer period and as well save your money in the long run.
You can choose to add a stabilizer after chlorinating your pool. Still, most chlorine products such as trichloro tablets and dichloride granules come with about 5% stabilizer infused in them to keep your chlorine level at normal. Only the Cal Hypo tabs are stabilizer free and may require a separate stabilizer.
If you are treating your pool with the trichloro tablets and dichloride granules, make sure you monitor your stabilizer level closely. Too much of it depicts its purpose and can invite green algae and bacteria in your pool.
Most people prefer diluting their chlorine in liquid and add stabilizer when need be.
How Much Stabilizer Do I Need for My Pool?

The good question to know the amount of stabilizer needed gets so confusing as some experts proposed quantities vary. Well, the standard says your stabilizer should fall between 30ppm-50ppm. Most experts would say 80ppm could be the maximum, but this proposes a great risk to your water. I would not advise you to stick to that recommendation.
Even though your pool is stabilized at 50ppm or lower, you still need to monitor your water and do regular pool testing. The idea is to keep your water sanitized at 7.5%, which implies keeping it at 3-4ppm when the water is stabilized at 50ppm.
To treat your pool with a stabilizer, you should use about 4 pounds of cyanuric acid for 10,000 gallons of water in every 30ppm you need to maintain. Most of these instructions can be gotten in the products you purchase. Make sure to go through properly before adding chemicals to your pool.
How to Add Cyanuric Acid to Above Ground Pool?
You can choose to add your CYA directly to the pool or get it mixed in a bucket before application. But note that adding the CYA directly to the pool poses a significant risk to your pool liner and the skin. So, it would be best if you got your chemical mixed in a bucket before application to avoid liner bleaching and eye irritation. Like earlier said, do not pour your chemicals directly in the skimmer.

If you are using trichloro tablets and dichloride granules, you may not need to add additional stabilizers. If you do, you may experience a significant increase in the stabilizer, which is not good for your pool. If you need to have more control over how your pool is stabilized, get a chlorinating chemical with no stabilizer.
Here are a few tips to have when adding a stabilizer to your pool.
Step 1: Put on your protective gloves and eye goggles.

Step 2: Half-fill a bucket with a warm water

Step 3: Pour a dose of CYA into the warm water and mix. Check your product use guide on what quantity is needed to maintain a normal chlorine level. Remember, if you need to maintain 10ppm in a 10,000 pool of water, you would need 13oz of CYA

Step 4: Pour the mixed solution directly into your skimmer

Step 5: Switch on your pump after two hours of application and allow it to run to allow it to disperse the solution around the pool. Occasionally, perform a cyanuric acid testing.

Note: Your product may say otherwise in the application of CYA in your pool. Always check your guide written on the product before application.