I removed unnecessary HD elements from your skin as these have a massive impact on performance.
For other improvements, I'd recommend you to change 100s/50s to the dot-variant as found in WWW skins. The scorebar-ki elements aren't particularly needed as well but I doubt they make a big impact.
https://endaris.s-ul.eu/ewdTwtxA.osk You also have to consider that a lot of elements aren't active during gameplay so skinsize of 5MB or 10MB doesn't say anything about the performance on a map.
Other considerations:
Do I really need a sliderfollowcircle?
Do I really need a cursortrail?
If you don't do it already:
Play with interface off. (Shift+Tab)
Make sure to have the following settings in your options:
Reduce dropped frames: Off
Fullscreen mode: On
Letterboxing: On (unless your osu! resolution is already full screen)
Snaking sliders: Off
Background Video: Off
Storyboards: Off
Combo bursts: Off (this actually confuses me in your skin because you have skinned them, lol)
Hit lighting: Off (only turn it on for maps where you really need it)
Shaders: Off
Softening filter: Off
Background dim: 100%
If your machine is really that old, you may also want to try and check Compatibility mode and see if that helps with anything (uses DirectX instead of OpenGL for rendering, which might have better hardware support if it's that aged). Naturally try to have as little background processes running as possible, use Snappy Driver Installer to assure you have the best drivers accessible (can make a world's different on bad audio drivers specifically).
After you did all of that, observe your FPS counter while playing. Generally speaking, a lot of graphics card want to prove how awesome they are and try too hard if you put the frame rate on unlimited, resulting in a lot of dropped frames. Check if it runs stable with 240fps first, if not press "Open osu! folder" in the options, open osu!.YourWindowsUsername.cfg and edit the value on the line "CustomFrameLimit" to something your machine can handle. Restart osu! for this to take effect.