How to kill shrubs growing through a wall?

[MerylSqueak]

Our garden runs up a hill and is terraced with jig blocks of stone. It was done in the 70s . One wall has forsythia and buddleia growing through it. My plan (thought up by a gardener who came to do something else) was to cut it all back and inject it with weedkiller so it died inside the wall. There's no chance of taking it out without wrecking the wall. I now realise I don't know where to buy a big syringe. None local and all the ones online have no needle.

Any ideas? You can see the buddleia cut back in the middle of the photo.

I think there are stump killers you can get that you just paint onto the stump?

It might die just being cut back that hard in summer. Buddleia is fairly bomb proof, but have managed to kill one just by cutting it hard back right into old old wood.

This one says you can brush or spray it on www.gardenworld.co.uk/product/sbk-tree-stump-killer/

Most weed killers work by their leaves taking it in. So I’d wait for shoots and then just spray them.

You don’t need a needle, just drill some holes and inject the stump killer into those.

I would be concerned that injecting weedkiller may kill too much plant material and the killing off of all the roots andcstems might damage the wall more than the shrubs themselves do. It might be best to just keep cutting off new growth?

Thanks for your replies.
I'll have a look at the stump killer.
I did think I had killed it by pruning a month or so ago but suddenly this week all three patches grew like mad.
Ok @CatherinedeBourgh I didn't realize that was what be meant. Thanks

I was wondering about that@Flump9 but I was torn between thinking it was a possible solution and worrying it would encourage the roots to grow. I simply don't know.