If the impurity is dry, then it does not pass to the one that touches it. So you don't need another clean cloth. You just separate the clean clothes and shake once to remove any doubt.
Below is a Sahih Hadith from Sahih Muslim, Book 2, Hadith 566
'Alqama and Aswad reported:
A person stayed in the house of A'isha and in the morning began to wash his garment. A'isha said: In case you saw it (i. e. drop of semen), it would have served the purpose (of purifying the garment) if you had simply washed that spot; and in case you did not see it, it would have been enough to sprinkle water around it, for when I saw that (semem) on the garment of the Messenger of Allah (ﷺ), I simply scraped it off and he offered prayer, while putting that on.`
See also - https://islamqa.info/en/111904