Sorry i didn´t reply earlier, been busy with some stuff.
The items i find necessary to pick up that are off the path as to speak (more than 2 screens away) is the saber you mentioned at X 9 Y14 .
Red Lander in Area 2 at X1 Y14, and the Blue Lander at X3 Y14.
Then we have a shield power-up in Area 3 X6 Y23 (optional), get it by defeating the green leach.
X6 Y22 Red Lander.
X23 Y8 (Area 5) there´s a Blue Lander, i´m not 100% sure if it´s necessary to take this one, i did it in my old run just to be sure to have enough health later on.
The item is 2 screens away, so we lose some time there if we decide to take it.
X17 Y16 (Area 6) we get a Red Lander when defeating the red crab boss.
It´s totally necessary to pick this one up.
In Area 7, there are two shield power-ups, we get one by defeating a red crab boss at X22 Y20 and the other at X22 Y23.
Area 8, there´s only one item necessary to pick up here, and that is the Red Lander at X12 Y18.
Kill the red leach here.
I tried to avoid fighting this miniboss at first, but with only 400 powerchips, i ran out of them pretty quick while fighting the red Grimgrin.
So i would say picking up the Red Lander here is necessary.
Area 9 X2 Y0, Blue Lander after we defeat the miniboss.
I´m not sure if this one if necessary to pick up, it depends on how much health we have at this point.
From here on, i didn´t pick up any more items in my old run, i finished corridor 9, than death warped and went straight to corridor 10 without losing any frames.
Special weapons.
There are only two weapons that i found necessary to pick up, the saber and the double saber.
Like you said, it may not be necessary to max out any of them.
You can pretty much run through all bosses with a lv2 saber or double saber.
However, i think you must have a lv3 weapon to take use of the safety zone inside the bosses.
I could be wrong though, i just haven´t found a way to do it with a lv2 weapon yet.
But let´s say that we decide to max out the sabers, we are going to lose a lot of time by picking them up.
So i say, the lv2 sabers should be enough with 2 attack with our basic gun.
Shield power-ups.
Yeah which 4 do we take? there are 3 bosses we can choose to fight, the green leach in Area 3, the blue floating crystal boss in Area 5 or the blob in Area 6.
All of these bosses leaves a shield power-up after defeated.
It´s only necessary to fight 2 of the bosses, the one that is the fastest to beat.
From there on as i mentioned, there are two more in Area 7.
If we pick them up we now have 4 (5 totally)
We can also choose not to fight two of the minibosses (either the one at Area 3, Area 5, Area 6 or Area 7).
If we decide to avoid fighting two of these bosses, there´s another shield power-up in Area 9 X6 Y3, we dont need to fight any boss to get this one.
However, taking this one means we must avoid picking up the Blue Lander in this Area (X3 Y6) since it will cost us time to pick that one up.
My personal opinion here is to have 5 shields totally before corridor 7, the speed boost will take us faster to Area 9 than normal speed would with 4 shields.
Attack power-ups.
I would only take the one in Area 2.
These are my thought´s on which items to pick up on our way, what do you think?