Have you already checked your lens and sensor for dust? If not, don't clean them yet. If the problem is caused by dust, you may be able to use a photograph of the specks as a mask to guide their removal in your existing images. Also do not use any automated dust removal feature built into your camera until after you get a clean shot of the dust that you are able to successfully use to post process your existing images.
If the specks are fairly consistent across images, but you've already cleaned your lens and sensor, you can reuse a mask that you manually create for one image.
If the specks are moving around, they may still be caused by dust on your sensor. If your camera has in-body image stabilization, the sensels won't map directly to image pixels. This would make post processing the images more troublesome because you'd likely have to manually align the mask. (See How can I automatically digitally remove shifting sensor dust speckles from a large series of photos?)
Unfortunately, most automated ways of removing specks like these will degrade image quality. If the specks are limited to the sky, it is fairly straightforward to limit noise-reduction to desired areas with a layer mask.
The most time efficient way of dealing with these images would be to use them at reduced size, where the defect simply isn't visible. (Basically, ignoring the problem.) You can spend more time removing specks from only the images you really want to enlarge.