Take your pick. Amazon even recommends one just for you.
https://www.amazon.com/s?k=lightning+trigger+for+camera&crid=31YT55YIVMOAZ&sprefix=Lightning+Trigger%2Caps%2C388&ref=nb_sb_ss_ts-doa-p_3_17

Cotton Carrier, back packs are what I have always used.
PS the 1-4 canon is NOT heavy. A cotton carrier would work great. But, it wimp comes into play, I would strongly suggest a back pack, this would probably be your best option.

Day's old Glossy Ibis chick. Wakodahatchee wetlands.
Sony a1, Sony 600 f4 @ f4, 1/800 sec. iso 2000. Exposure was auto, taken in deep shade. I usually shoot all manual but when I switch quickly to all dark shade I switch to auto. Chick was about 40 feet from the board walk.
Focusing was small center spot placed on the chick.

Java Rice Finch Indonesia. Butterfly World Florida.

No toes stepped on. We are good.

That was one of my recommendations.

Florida Long Neck.

There is not a teleconverter made that improves an image, so, there is only one way to go with a teleconverter, and it's not a good thing.
Look, your Z-50 is an aps-c camera, so any ff lens you put on it will automatically get a bump in field of view.
So, put a prime 400 on your camera, and it becomes a field of view of 600 mm WITHOUT a teleconverter.
My suggestion, try the 400 on your Z-50, my most telephoto lens is a 600 prime, I do wildlife professionally, I need nothing more than that for 99% of my work.
800mm entails a lot of expert handling to assure a strong sharp image.
Do us all a favor and put your money into a 400 or 500 prime and do not pass go, and do not purchase a teleconverter.
BETTER SUGGESTION
Buy the Nikon 180-600, this lens will give you a field of view of 270-900mm. You will not ever need anything else for wildlife photography, this lens is much sharper than any Sigma lens on the market in a similiar focal length.
Read the reviews on the Nikon 180-600, they are very good for a lens under 2 grand.
Plus, a zoom is more versatile than a fixed prime.
In the field I use the Sony 200-600 for much of my work, I do have a 600 prime but within a 100 yards, it is really hard to tell the difference between the two.
Below is an image with the 200-600.
If I were you I would consider this lens, the Nikon 180-600 as your go to wildlife lens.
Good luck and keep on shooting until the end.

Negatives will last how long buried in atomic waste?
Flash drives, external drives, hard drives will last how long buried in atomic waste?
How the F caries.

They'll have to pry my flash drives from my cold dead hands.

Who stole the cookies from the cookie jar, Number 1,stole the cookies from the cookie jar, WHO ME? YES YOU? COULDN'T BE, THEN WHO? number 2 stole the cookies from the cookie jar, WHO ME? YES YOU? COULDN'T BE, THEN WHO? Number 3 stole the cookies from the cookie jar, WHO ME? YES YOU? COULDN'T BE, THEN WHO? Number 1 stole the cookies from the cookie jar.................................................................

When your a black bellied whistling duck, there is no much to do hanging with the brothers all day long.

Interesting thought. Yes, I do agree, their are slight color differences between OEM lenses.
For instance, I have always loved facial colors brought by Nikon lenses.
I have always liked fall leaves using older AF Minolta lenses.
I really like wildlife images by Canon lenses.
In fact, I still have several Minolta lenses I still use in the fall on my Sony a1 and a9 bodies.
Good luck and keep on shooting until the end.

This fine, outstanding, wonderful, super spectacular, great, fantastic, Nikon 10-20 mm lens will give you an field of view on your D3400 of 15 to 30mm. It is refurbished, which will save you even more money on this fine, outstanding, wonderful, super spectacular, great and fantastic lens.
https://www.bhphotovideo.com/c/product/1386310-REG/nikon_20067b_af_p_dx_nikkor_10_20mm.html