Whilst a machine polishing session is always going to be the best and most effective solution to your problem, if they are only very light as you describe then it's not impossible to remove this level of defects by hand.

Menzerna 203S is highly effective by hand in addition to being a great machine polish.

Head over to Detailing World and do a search on hand polishing - you'd be surprised at what's achievable with the right products and techniques, although it is very time consuming and labour intensive work by hand.