You're talking about using one of these?

https://www.rcworld.co.uk/acatalog/2-4Ghz-400mm-Extended-Aerial-Pair-P_RA2_4G_400.html

or on ebay...

https://www.ebay.co.uk/p/Futaba-2-4ghz-400mm-Extended-RX-Aerial/1504309322

So long as these are the advised spec by the manufacturer, why worry about the impedance?

You might be interested in this discussion I had a little while ago on the Single Channel site about replacing 2.4Ghz aerials - points Martin made include:

"......I tested all my detachable 2.4 GHz antennas and found quite a wide range of frequencies they were best tuned for, ranging from about 2.1 to 2.6 GHz - but they all work fine and have pretty good SWRs at the 2.45 GHz point.

What was more interesting was testing various antennae that I've received for various pieces of kit over the years that run at 433 MHz, 5.8 GHz and the GPS frequencies of 1.2 and 1.6 GHz. Many of these are just 2.4 GHz antennas - I even have one that is labelled 433 MHz, but is really a 2.4 GHz and quite useless at 433 MHz!......."

".....It is important to realize that all the coax cables we use (all relatively light and thin) are all quite lossy at 2.4 GHz, so you shouldn't make the non-transmitting (intact cable) part any longer than it needs to be. if you have a foot or two of coax feeding the active part of the antenna (the modified bit at the end) then you can easily lose half of the available signal....."

http://mode-zero.uk/viewtopic.php?f=52&t=389

I would also add that polarisation may become important when you have an aerial close to a horizontal reflective plane like a lake. I suspect that you might get a lot of the signal coming at you horizontally polarised, which a vertically mounted aerial won't like.

For video output from a boat I've been using the circular polarised aerials that the drone operators use in an attempt to maintain signal at distance - https://www.ebay.co.uk/itm/2-4GHz-Circular-Polarized-clover-leaf-Antenna-set-with-short-connector-RP-SMA/253889968333?hash=item3b1d0578cd:g:YkEAAOSw5LZcZF3Y:rk:3:pf:0

Hi there, I presume that you are referring to 2.4ghz radio system. I have various models using 2.4ghz and have not had to extend the reciever aerial on any of them. Most only have about 50mm above the deck and I've been in full control up to 300 mtrs (28 acre lake) with the older 27mhz. Or 40mhz I have to have a fully extended aerial to get a good reception at distance.
Hope that this will help you.
Cheers Colin.