‘All batteries are hazardous waste’ - to all intents and purposes, and as far as any member of the general public is concerned, this is exactly what batteries are, and should be treated as such. they are NOT something you just throw out with household rubbish without batting an eyelid. better safe than sorry.
second the above comment - the tape should stay attached to the part behind the fan. it's fiddly but the best way.
also, if you want to save yourself 50 dollars and the delivery time just take the fan apart - two screws release the housing and the fan itself just pulls out of its bearing. clean off all the dust, apply a couple of drops of penetrating oil (wd40, kroil etc) to the shaft of the fan and reassemble. good as new.
* this slides out sideways, in the direction of the ribbon. obvious when you know, otherwise it looks like the entire connector is just a single metal piece. there are two tabs which stick out at the sides of the moving part closest to the ribbon. the fixed part of the housing - the metal box - stays put.
* it's very tight, so persevere and just do each side a little at a time, it eventually slides out. i have big hands but managed to get the nails of my thumb and forefinger hooked behind the tabs to ease it out.
this is a difficult step with unclear instructions. if you can, take magnifying glass or lupe and have a good close look at the connectors before trying to remove them.
small connector:
* this has the word PUSH on the top side. this means 'push down to connect' so to disconnect it needs to come straight up.
* the connector housing is divided into two parts - a fixed rectangular housing like a box with the top and one long side missing, and the part attached to the wires which looks like it is divided into two - a small part split into four sections adjacent to the four wires, and the part with the word PUSH on it - but is actually one piece.
* to disconnect you need to get in the tight gap between the two parts and gently pry up. i found it easiest to do each side a little at a time until it pops off. i used a scalpel (probably not advisable) but i have a steady hand and the sharp edge is ideal. be warned, if you slip you will likely damage something so take care.