Any Pine should be safe as long as it is very well dried, no gum oozing out of any knots in and not treated. The sap is not good. Stay away from any pine wood with knots in it. These may bleed sap.
Sparrow. You are in an area where there is a tree that is one of the best you could use.
It is an invasive Aussy (common name here is Paperbark Gum) and cutting any branch from this should not get you into any trouble as they want them gone from the everglades.
It has a parchment like bark and is a very hardwood.
All parts off this tree may have beneficial things for our birds from chewing the flowers and seeds through to chewing the bark.
The joy with this tree is you can just cut a clean branch and give to your birds. You do need to know it is free of bird pooh, urban pollution, and any chemicals. Do not strip the bark! That is the birds job.
Bottlebrush is very close to this tree.
I will post a few photos of this tree, it's flowers and it's bark for you.
An end shot of a branch
Some of the bark peeled off