There's a lot of options. For sure, if your applicator has some 'pick', it'll help you getting the job done better.
In example, LC CCS Hand applicators,
CCS Euro Foam Hand Applicators Trio - Your Choice!
The orange will offer more cutting power if you're trying to remove some defects, the white will be good for finer polishing, or even the compound on soft paints.
i.e, I'll use very well known products, meguiar's Ultimate compound and polish.
You can use the compound with the orange applicator, polish with the white.
Sure you can use any combination that fits the job after trying a test spot.
The 'inexpensive' Meguiar's Even Coat Microfiber applicators are also a good choice. They offer a good grip and the 'pick' of the Microfiber helps getting good results by hand.
Meguiars Even-Coat Applicator - 2 Pack: 2 microfiber applicator pads that are excellent at applying Meguiars products.
A Microfiber towel may work as well if you have good technique (fold it at least in 2 to get some cushion, DON'T exert pressure only on fingertips, but spread pressure evenly)...
Generally with Microfiber applicators, the 'Additional Cut' will be provided by product use, I may use either Menzerna FG400 or SF4000 with MF applicators and get correction with one and good finish with another.
There's a lot more options, like using small pads with a gripper, like polishing pal, etc...
I Have to go now, do a research and you'll find the one which fits your needs.
Also look for Mike Phillips's polishing by hand tips and tricks around the forum. Put some 'passion' behind the pad, move your hands at speed of light, some elbow grease, and you'll be good to go!
Kind Regards.