I suggest the following route.
(1) Shinsaibashi (N15) -> (N16) Nagahoribashi by Osaka Metro.
At Nagahoribashi, Car No. 4 should be convenient for your transfer.
(2) Nagahoribashi (K16) -> (HK63) Awaji
by Metro - Hankyu through service.
At Awaji, you make a transfer via the same platform.
(3) Awaji (HK63) -> (Hk81) Katsura by Hankyu.
(4) Katsura (Hk81) -> (HK98) Arashiyama by Hankyu.
https://subway.osakametro.co.jp/img/osakametro_rosenzu_20250404.pdfI think you can make the first two transfers
more quickly and more easily
than the one transfer at Umeda (shown below).
The Hankyu platform at Osaka-umeda is on the 3rd floor,
vertically away from the Osaka Metro platform on the basement.
At the subway Midosuji Line platform,
Car No. 8 should be close to the elevator.
You go up to the pathway,
exit Osaka Metro through the north gate,
turn to the right,
go into Hankyu Osaka-umeda Station,
go up to the concourse,
enter Hankyu through the gate,
check the departure track number of your train,
go up to the platform,
and catch the train.