I don't think that is a good idea.
The flexibility in the wood is from from itself (species) & it's moisture content - perhaps ~10-12%.
Oil will not replace that if has dried out .... but I am not a bowyer!
I got lucky with my FH Ayres bow, but didn't do as much due diligence on the the nocks
as I should have, ultimately leading to a nock coming off at full draw & the bow breaking :-(
With these old (long)bows you really do need to do your "due diligence"
- examine it carefully: sight; touch/feel; the wood & the nocks - I believe horn dries out too/dessicates & splits,
as happened to mine :-(
- secureness of the nocks - old glues deteriorate, I reglued one of my nocks, the one that came off.
Wrong glue most probably, slow drying epoxy might've been better that whatever I used ;-)
Once all seems ok, you'll need to teach it to bend again .... just like it was tillered in the beginning
- nice "soft" Dacron B55 string .... go slowly ....
....or maybe just keep as wall hanger?
How do you know date? To me looks like pre-1906 as it doesn't have the "Ltd." after "F.H. Ayres" when co. passed
from father to son ....