Can you skip numbers with math.random?

Technically
No, not really.

In this particular case, you can do

math.random() > 0.5 and 1 or -1

which selects 1 or -1 with a pretty equal chance.

As a more all-round thing, you can use tables to do this. If your numbers you're skipping don't fall into some mappable rule, you can just put all the numbers you want to be able to pick into a table and select from that table instead.

local numbers = {
 6,
 24252,
 39231283,
 2
};
local selectedNumber = numbers[math.random(#numbers)];

selectedNumber would become a random number from that list.