I tried to research the topic and only came up with a cup that's 1/2 full for an answer.
Someone on the 1858 Forum said that his research comparing the flat Uberti and Pietta trigger/bolt springs indicated that they were different.
And he went on to make his own wire spring using wire benders. --->>>
https://1858remington.com/discuss/index.php?topic=4478.0
Questions asked of Wolff Springs said that they didn't know which of their springs would work since they are all labeled to specifically fit Colts.--->>>
https://www.n-ssa.net/vbforum/archive/index.php/t-267.html
However it is suggested that because the Colt and Remington trigger and bolt parts are so similar that pre-made wire springs can be used and adapted for the Remington if necessary, but without giving any specifics regarding which spring to order. --->>>
https://civilwartalk.com/threads/up...olver-to-a-music-wire-sear-bolt-spring.96785/
You've probably come across Smokin' Joe's pastie about how to make the Colt trigger / bolt spring from a safety pin. It doesn't cost much to try to make one to fit the Remington. --->>>
https://www.thehighroad.org/index.php?threads/cylinder-bolt-spring.623759/
Even Wolff makes both types of Colt springs, flat and round wire. Some have said that changing to wire is not always preferred, even though wire usually doesn't ever break. But they may need adjustment over time. --->>>
https://www.gunsprings.com/index.cfm?page=items&cID=3&mID=1&dID=96#403
Unrelated unless desiring a lighter trigger pull for the Remington, is a thread that indicates a direct Wolff replacement mainspring for the [Pietta] Remington 1858 which will lighten the trigger pull more favorably than by replacing the flat trigger /bolt spring. --->>>
https://1858remington.com/index.php?topic=5248.0
"IMO one should stay away from trying to lighten the bolt spring section. The bolt needs a good lockup especially with the shallow bolt groove of a conversion cylinder. You might try bending up the portion that is the trigger spring part to lighten trigger pull. Having said that, the most effective method to lighten a trigger pull, other than messing with the sear, is to install the Wolff 32280 hammer spring."
To conclude, I can't find a thread indicating a direct replacement Heine or Wolff wire spring that actually fits the Remington 1858.
Some folks make their own while others have either "maybe or probably" adapted the replacement Colt wire springs to fit their Remington.
There's nothing definitive that I found, only suggestive that a factory wire spring should be able to be tweaked to work.
Perhaps that lack of concrete information is why people end up bending their own music wire if they really want one.
The info. has probably already been posted somewhere on the internet waiting to be found.
If anyone can confirm which wire spring to buy and post a reference to the thread then that would be very helpful to others.