On my board, can I attempt to use my hand plane or would I maybe mess it up? I think it's a number 4
You could 'test' your plane on the bottom side of the top where it will NOT be seen to see for yourself how that may or may not help you here... It all depends... Would be worth a 'test' in my opinion to see if it could save you any time.
As narrow (yes it is long but still not very deep) as it is you 'could' easily knock it down with some 60 grit sandpaper. and then move on to your finer grits before you start your finishing.
The Dewalt 5" orbital sanders are relatively cheap (can be SUPER CHEAP if you check local pawn shops for one that is used), you can get the papers in many different grits, and they even have a dust collector thingie that works somewhat well (can easily attach a small shop vac hose to the fitting and make even LESS dust)
The Dewalt orbital sanders are VERY sturdy and will last a LONG time if you take care not to damage the hook and loop pad. Even if you do manage to someday kill the hook and loop pad you can get a replacement kit from the Dewalt store that includes a new base pad + the gasket thing that goes between it and the sander for CHEAP. You will want to save any basepads that you DO eventually kill so you can sand the hook and loop stuff completely off of it and use that pad for 'stickyback' paper just in case you ever end up being forced to buy that kind (because sometimes that paper is cheaper than the hook and loop).
You also mentioned previously that you had a bookcase going on top of this top... Depending on IF the bookcase has a 'floor' or 'bottom' in it and how long and deep the bookcase is will also help determine how much you really 'need' to sand down. No need in finish sanding parts that will be covered up and will not be seen. Need to know more about your bookcase to determine how much you 'need' to sand.
Just guessing here but based on your previous pictures and how close you managed to get your joints - I would guess it would take no more than a few hours to flatten the entire top out on the topside if using 60 grit paper. The bottom of this will never be seen so there is not much 'need' to finish that very much.
That would be less than an hours worth of work with a good beltsander and some 80 to 100 grit paper but those cost a bit more than the orbital would...