Add a custom tool:
1) Player selects entities with a free custom tool (no resources/tech required to craft it)
2) The variables replacement dialog pop-up
3) Player changes signals mapping...
4) Player clicks "apply" and it replaces signals in the previously selected entities list
Note: Check entitiy.valid here — someone/bitters can destroy/deconstruct these entities between steps 2 and 4.

So, Player can copy-paste some elements, and cancel the replacement mapping popup.
Then, if Player is ready, it can re-select all entities and replace signals.

That's a great idea!

However, the variables are currently designated by signals. Meaning once the signal is replaced, the variables are lost. This tool would only benefit you if you canceled the original apply screen or built the entities and configured them with variable signals by hand.

Ultimately a cut-and-paste in the same spot would achieve the same goal.

Knowing that, do you think a tool like this would still be valuable?

I think so. Scenario: place multiple DIFFERENT blueprints with shared vars, cancel popup in the progress. Then at end replace all vars at once.
Blueprints like:
- unload station (resource A) — variants: from AAI Cars, from Trains
- load station (resource B) — variants: to AAI Cars, to Trains
- resource processing station A->B — variants: smelting schemas for ores, different assembler schemas for ingredients.
Mapping:
resource A — variable 1
resource B — variable 2

They are shared between all these blueprints with partial schemas

I noticed that my blueprint dialog did not appear when placing the blueprint from map mode.
It can be temporary issue or something...
So, I think we NEED this tool... at least as a workaround in many cases.

I think this is related to the blueprint library issue. It's working in v0.0.4 (I'm about to get this uploaded to the mod portal)