As the title suggest, I recently did a conventional 8 man booster draft with just four players, each of course making two decks. It sounds like madness both logistically and in terms of game complexity. In practice it worked smoothly and without issue and is absolutely something I will do again.
Normally drafting with fewer than 8 is fine, especially if you reduce booster size and chuck in some extra packs. I have done plenty of drafts with five people and had 5 packs of 9 cards per player. Sure, you end up with 54 cards instead of 45 but you see fewer cards overall so the quality is roughly the same. When reducing pack size too much you start to get awkward variance in packs which leads to more non-picks than is ideal. You can combat this by increasing pack size but discarding the final few, so say packs of 12 but still only picking 9 of them total. This does also increase the quality of the decks but mostly just helps to stop getting that all white pack when you are not in white... You can seed packs to have a colour spread if you like to fix this instead but it that takes a lot longer and has never felt worth the effort to me. As a general rule things get trickier the fewer drafters you have. Seven is fine and needs no tweaking. Six is fine but you do notice that it is a small table. Five is workable but needs some extreme tinkering to get the right feel. Four has always been tough and always results in some form of exotic draft rather than the conventional booster method.
When faced with four people wanting to draft someone bravely suggested a method of doing so as if 8 and it was great. We made up 24 packs of 15 cards as if a normal 8 man. We then allocated the deck numbers to each person. Seat one would draft decks 1 and 5. Seat two taking 2 and 6 and so on and so forth ensuring you were always sat opposite your other deck as it were. We then took two pieces of A5 paper each. On the first we simply had our two decks, say 3 and 7 in my case. This is where I would place my picks so as to not get confused. The other bit of paper was labelled for the passes and would read 3 - 4 and 7 - 8 on my left and 2 -3 and 6 - 7 on my right. This is where we would pick up and put down packs so as to keep track of where they would be going. We would then draft a pick for our lower numbered deck first and then the higher numbered deck. For me the sequence would be pick up the pack in the 2 - 3 pile, place my pick in the deck 3 pile and place the rest of the pack in the 3 - 4 pile. Then pick up the pack in the 6 -7 pile, place my pick in the deck 7 pile and the rest of the pack in the 7 - 8 spot (when passing left). Everything simply reverses when you pass right. Then you just draft as normal but being two people at the table and thus winding up with two separate pools from which to make two decks.
As for the games doing a round robin would mean 6 matches per deck and 12 per person we elected to do an elimination bracket. This can be single or double as you desire. You want to have all decks 1-4 in one half of the bracket and decks 5-6 in the other half so that you can only meet yourself in the finals.
There were some added complexities within the draft as you might expect. You obviously had a lot more information to work with and a lot more relevant information you want to retain. You see packs sooner, twice as often, and will be considering picks for two separate pools! Pretty mental to try and do to high standard where you can remember everything but none the less it worked surprisingly well. Everyone had good decks and were in good seats for those colours. Going a bit more on intuition and feel seems like the best approach, certainly for someone with decent draft experience. Comfortably the best way I have found to do a normal (as possible) booster draft with just four players. Well worth a try. A lot less confusing and extreme that it appears at first glance. Quickly it felt quite natural to draft that way and there were no mistakes with passing or packs either.