Not for a ranged weapon build, especially not with the Biohacker class.
In terms of ability scores and HP, the Raxilite's size is baked into the mechanics of the race in a balanced way. You pretty much enumerate the relatively few mechanical advantages and disadvantages associated with tiny size. Note that not having a reach basically makes combat maneuvers impossible since the opponent must be within your reach (CRB p. 246); though I don't imagine you chose Raxilite or Biohacker so you could run around bullrushing opponents.
As for weapons, a tiny character can use medium sized weapons, though there is a -4 penalty to hit, which is a serious handicap. The Starfinder Near Space Guide introduces the Giantblood theme. A character with this theme, at 6th level, can use weapons for characters one size category larger with a -2 penalty instead of the usual -4 penalty. This is still a disadvantage, but not as bad.
Longarms generally do greater damage than small arms, but small arms damage scales up okay. Plenty of medium-sized characters prefer small arms for various reasons and use them into the higher levels. Miniaturized weapons do not do less damage like they do in Pathfinder (and probably they should), so getting miniaturized long arms or heavy weapons doesn't hurt you mechanics wise; however...
Paying 2x for specially-sized weapons can be a problem for a Starfinder character. The CR for monsters is geared almost as much to item levels as it is to character levels, so it is important to keep your weapon item level on a rough par with your character level and this costs money. By the time weapons get to item level 10-12, they cost tens of thousands of credits, and doubling that can be a big deal. If the rest of your party isn't interested in giving you two shares of all the loot, it will be hard to keep up with them over the long haul. This is a disadvantage for a class where weapon damage is very important, but not too much of one, since you can used normal-sized small arms.
The problem becomes even less significant in your case because you want to be a biohacker. Biohackers generally rely on the effects of serums they inject into their opponents and allies with injection weapons (the Character Operations Manual, which introduces the biohacker class also introduces a plethora of ranged injection weapons), so damage becomes kind of secondary and having an injection weapon a few levels behind your character level becomes less of a big deal. Yes, injection weapons do damage and the best longarm injection weapons do a bit more than the best small arms injection weapons, but the effects of what you're injecting is what makes the class special, so again, sticking to small arms shouldn't hurt you that much.
For a melee build, being Tiny is a crippling disadvantage.
As you point out, the reach of a tiny character is 0, which means that for melee attacks they either need a weapon with the reach special property (vastly reducing choice of weapons), or they must enter their target's square and possibly provoke an attack of opportunity. Further, since they threaten no squares, they cannot control movement through adjacent squares via attacks of opportunity the way a larger character could. Enemies can move right past them with no risk. Finally, according to the rules, tiny and smaller characters are incapable of flanking opponents or even helping an ally flank an opponent. These disadvantages would put a tiny melee fighter at huge disadvantage.
