What do you call a person who reconnoitres?

Scout is the common word for that. — M-W

1.a. one sent to obtain information; especially : a soldier, ship, or plane sent out in war to reconnoiter

But the exact answer is the obsolete word reconnoiterer (noun) — TFD, Dictionary.com

_{Usage examples provided by @deadrat:}

From Vienna in 1848 by H J Coke (1849)

Now and then the sentry fires at the incautious reconnoiterer, till all is hushed!

From Stasi: The Untold Story of the East German Secret Police by J O Koehler (1999)

The film extolled the virtues of Horst Hesse as a "heroic comrade," a "reconnoiterer for peace" who had insinuated himself into a U.S. intelligence service.

_{Related words: lookout, lookout man/woman, outrider, advance guard, vanguard, spy; avant-courier}

If you wanted to be fancy, you could use reconnaisseur, which would be the correct French. (Wiktionary also shows "reconnoisseur" in a sixteenth-century source.)

A scout or reconnoiterer is the word you are looking for. But if you want to use the word for someone who does reconnaissance during flight, you could use air observer which means:

An air observer is a military aircrew member whose duties are predominantly reconnaissance. The term originated in the First World War in the British Royal Flying Corps, and was maintained by its successor, the Royal Air Force.

The term is still used in some contexts now, such as police helicopter units.

[Wikipedia]

There doesn't have to be a word for someone responsible for the execution of the act (for example what is the person who radios called?) In this case English doesn't have such a word.

Reconnaissance is a common word in the military; the person responsible for its execution is typically named using a Noun Adjunct. As an example, look at the naming in http://en.wikipedia.org's reconnaissance page: https://en.wikipedia.org/wiki/Reconnaissance

• Reconnaissance Asset
• Reconnaissance Batallion
• Reconnaissance Company
• Reconnaissance Detachment
• Reconnaissance Officer
• Reconnaissance Platoon
• Reconnaissance Squad
• Reconnaissance Team Leader
• Reconnaissance Unit

You can use "recon", as in:

I'm a saboteur

I'm a spy

I'm recon

It's a bit of a quirk of english, and I suspect that this usage is probably not grammatically correct in a technical sense, but it's not unusual for a person to identify themselves as being what they do, albeit sometimes with a qualifier (I'm recon guy* or I'm the recon guy**). You'll particularly see it in military fiction (I don't have the experience to know if it occurs in real-life military).

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* see also: buffyism/wheedonspeak

** guy is non-gender-specific