Honestly, I wouldn't be worried so much at all about the pesticides from the ground, as most of them are very short-acting and dissipate quickly. Unless this tree was directly sprayed, and sprayed recently, then this isn't the biggest issue you face at all. What you do need to worry about are all of the microscopic parasites and the microbes that live in the wood. There are a great number of microbes, specifically a lot of different fungi and bacteria, that live inside the wood of trees; stripping the bark off is fine to do if you can't bake the branches (I always leave the bark on and bake the branch, so that my birds can have the fun of stripping the bark off themselves, they love it). But even if you strip all of the bark off of the branches, that isn't going to do anything to kill the microbes that are living inside of the wood. And the tree doesn't have to be alive for most fungi and bacteria to survive and live inside the wood...That's why baking and/or deep-freezing is the best way of disinfecting it.
No, just spraying the branches down with F10, bleach, or anything else is not going to do it, and this is why people soak the branches overnight in the disinfectants, as they need to be able to soak-through the branches in order to kill the fungi and the bacteria that is living deep within the branches. Any of the companies that commercially sell natural bird perches or the natural branches to make perches from, such as Manzanita branches, bake the branches with the bark on, as it's not the bark alone that is the issue, it's what is living inside of the wood branches. There are some microbes, specifically some fungi, that live and thrive off of dead wood...and if I recall correctly, there are also some protozoa that also live specifically inside of the dead wood, however it's the fungi that are usually a problem, along with some microscopic parasites, such as certain mites. This is why it's necessary to either bake the branches so that the inside of them is heated to a high enough internal temperature to kill all of the microbes living deep within the wood, or to freeze the branches through to the middle of the branches, same principle...And if you soak a branch overnight in bleach, the bleach also penetrates through to the middle of the branch to kill the microbes within, which is why it's necessary to soak the branches in clean water overnight, and keep changing the water and soaking them overnight several nights in a row, to get all of the bleach out of the middle of the branches. Then it takes them several days to weeks to completely dry out, but it works (I don't know if soaking them in F10 and water overnight would penetrate through to the middle of the branches and kill the microbes inside or not, you're better off using a mixture of STRONG bleach and water and soaking for 24 hours, as this is known to work).
I would not just strip the bark off and then spray the branches down with F10 and then rinse them, as this will do nothing to kill the fungi and bacteria living inside the wood that could potentially make your birds very sick, or worse. There is a reason that these techniques are used by commercial companies and private wooden perch builders, such as heating or freezing the internal temperature of the branches all the way through, or soaking the branches all the way through with a strong bleach solution, and then properly soaking clean water through the branches several times to rinse the bleach out of the inside of the wood. It's not something that you want to just "wing", as there are some really nasty, dangerous fungi and bacteria (mostly fungi) that live inside of trees, both living and dead. Spraying them with F10 is not going to help much at all.
If you can't bake or deep-freeze the branches (not a regular freezer, but a commercial deep-freeze overnight), then you need to find something large enough to put them in and soak them for 24 hours in a strong bleach and water solution, and then do the same in clean water for several nights/days in a row to get all of the bleach out of them. This is the only way you're going to kill everything that is living inside of the branches.
