If you're looking for a tap splice, there's basically no such thing for Code electrical. You need about 9" of slack for each end of each cable in each box, so your options are as you see them.
put the box at your location, and replace whichever half of the original run is easier to replace. (Plan before you cut!)
Divert that circuit in some useful way through your new work.
use a Tyco inline splice to avoid a second box just for the splice, but those splices are untrusted, so generally Code doesn't want you doing that unless there's just no other option. Even the Tyco splice consumes some length, and it doesn't let you tee.
last resort, put 2 boxes at least 18" apart, and add a short length between the boxes. Bonus points if you go farther apart to place them at potentially useful future locations.
Make sure ALL the wire you are adding to the circuit is at least as large as the wire currrently in the circuit. If you have even one inch of 14AWG in a 12AWG circuit, you must downgrade the breaker to 15A, which is a waste.
Wire-nutting produces a fine and durable splice if you firmly tighten, use the right size (yellow is fine for 2-3 of 12-14 AWG). And use modern wire nuts (don't reuse really old ones, as the quality has improved in leaps and bounds). Of course any splice needs to be in a box, I recommend a metal box because if there's arcing in the box, it won't burn through, and will conduct heat throughout the box so the box doesn't get hot enough to set wood on fire. If arcing gets hot enough to overwhelm a steel box, the breaker will have tripped.