before polishing - if you haven't already - i'd recommend 'claying' the paint. this process removes any accumulated, stuck-on grit and grime like tree sap and bugs, that may not come off with normal washing. you require the clay, plus a suitable lubricant, which is typically in the form of a spray-on quick detailer. for example, you can use Meguiar's clay + Quik Detailer:
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have plenty of clean, quality MF (microfibre) cloths handy when polishing/cleaning.
to hand-polish, use a 'foam applicator', which is a small disc of closed-cell foam, for this very purpose.
you can slightly moisten the applicator with a mist of quick detailer for starters, until it absorbs some of the polish. they can be cleaned in the washing machine (same with MF cloths; you can also buy proper MF 'cleaning detergent' to use in the washing machine if you wish, but not crucial).
for polishing-sealing, i would recommend AG (Autoglym) 2-stage products which suit hand-polishing:
1. Super Resin Polish Autoglym - car cleaning products, car care products, car valeting, car detailing
2. Extra Gloss Protection Autoglym - car cleaning products, car care products, car valeting, car detailing
the SRP - as its name suggests - is the polish to 'remove' swirls. in general, such products can do it in 2 ways: 'cutting' the clearcoat to make it smooth, and 'filling' the swirls to bring them level with the clearcoat to also create smoothness.
the EGP is the sealant - with no cutting/polishing properties - to add a layer of hardness/protection and gloss.
whilst i've not used these, from all reports they are as good as you'll get for hand polishing. you can apply firm pressure with the pad. don't stress, cos you're unlikely to achieve anywhere near the same pressure/heat as a machine polisher will, so the chances of going 'too far' is remote. you may want/need to do each panel twice with SRP, depending upon severity of swirls.
however, if this still seems too OTP (over the top), then consider an all-in-one product. these typically contain 'filler' to hide swirls plus a wax or synthetic sealant for protection and gloss. they tend not to have cutting polish, so will NOT remove the actual swirls, and merely try and hide them. 95% of people are usually happy with such a product, and these include:
*Meguiar's NXT Gen Tech Wax
*Eagle One Nanowax
*Duragloss Polish & Cleaner #101
*Poorboys Polish with Sealant (will 'cut' if used by machine)
if buying AG, i also recommend their Bumper Care product for black plastics/trims, like the window frames, wiper blades, and plastic wiper panel at the base of the windscreen.