Step 1: Interpreting the instruction.
The problem requires us to combine the two sentences into one complete sentence without using the conjunctions and, but, or so. Hence, we must use another grammatical structure such as a participial phrase.
Step 2: Evaluating the options.
(A) uses the conjunction and, which is prohibited according to the instruction.
(B) "Packing up the bundle" alters the intended meaning slightly because "packing up" suggests arranging or organizing, which is not stated in the original sentence.
(C) "Picking up the bundle, he walked away." appropriately uses a present participle phrase to combine the two actions into one sentence without using forbidden conjunctions. It preserves the original meaning accurately.
(D) "He walked away by picking up the bundle" alters the intended meaning because it implies that walking away happened because of picking up the bundle, which is logically inconsistent.
Step 3: Final Conclusion.
Accordingly, the appropriate sentence that combines both statements properly without using and, but, or so is option (C).