It could all explode in our faces.

It's usually an exageration, sometimes when you make plans things go horribly awry. It's hard to tell exactly what they are taking about here, but if it's about wiring, I'm going to assume electronics or something involving electricity and in this case, if the wiring isn't correctly done, bad things could happen. If it's about a bomb, it could literally blow up in their faces if they mix wires or in the case of dismantling a bomb if they cut the wrong wire it will blow up.

Is this from literature written in the past? If so, the second sentence give a clue: the "wiring" is talking about sending a message. Today, we would say, "email".

It could all explode in our faces.
It would be wisest to delay wiring it as long as you can.

This person means: This could all turn out NOT like we want it to. In fact, it might cause a big fiasco. Delay emailing him about the issue as long as you can.

Have you ever had a "blow-up" with someone about something?

If a plan went badly wrong and produced catastrophic results for the perpetrator you can say it blew up in his face.

Blow up means explode.