x = "The 'quick cunning brown' fox 'jumps up and over' the lazy dog"
gr <- gregexpr("'[^']+'", x)
mat <- regmatches(x, gr)
regmatches(x, gr) <- lapply(mat, gsub, pattern="\\s", replacement="_")
x
eCA9ICJUaGUgJ3F1aWNrIGN1bm5pbmcgYnJvd24nIGZveCAnanVtcHMgdXAgYW5kIG92ZXInIHRoZSBsYXp5IGRvZyIKZ3IgPC0gZ3JlZ2V4cHIoIidbXiddKyciLCB4KQptYXQgPC0gcmVnbWF0Y2hlcyh4LCBncikKcmVnbWF0Y2hlcyh4LCBncikgPC0gbGFwcGx5KG1hdCwgZ3N1YiwgcGF0dGVybj0iXFxzIiwgcmVwbGFjZW1lbnQ9Il8iKQp4Cg==