That's そっと, not そつと.
そっと is an adverb, meaning, softly, carefully, gently, quietly, etc.
そっとする is an idiom, meanig "to leave it as it is", and ~ておく means "to keep it as it is" here.
おこう is the volitional form.
Thus, the given translation comes form what the speaker is going to do; keeping what they are doing now(walking) and leaving what they saw as it is (staying away from it).