1. We should settle the dispute through negotiations without resorting to legal proceeding.
我們應該通過仲裁解決爭議而非法律途徑。
還能這樣說：
We should negotiate the dispute instead of resorting to legal proceeding.
We should not resort to legal proceeding but take the way to negotiate the dispute.
應用解析：
settle a dispute with sb. 同某人解決爭端；
settle disputes between 調解……之間的爭端；
dispute with sb. about 與某人爭論某事

2. We prefer to resolve disputes by amicable, nonbonding conciliation between two parties.
我們愿意雙方友好、互相諒解地解決爭議。
還能這樣說：
We would rather settle the disputes between two parties with an amicable and nonbonding conciliation.
We two parties settle the disputes in a friendly way with mutually understanding.
應用解析：
make a resolve to do sth. 決心做某事

3. If any dispute should arise over the inspection, we may submit it for arbitration.
如果是檢驗引起的任何爭議，我們可接受仲裁。
還能這樣說：
Any dispute caused by the inspection can resort to arbitration.
We may submit the dispute which arises over the inspection for arbitration.
應用解析：
arise from/out of 由……引起，由……而產生，從……中產生

4. If you are not prepared to compensate our loss, we suggest that case be submitted for arbitration.
若你們不賠償我方損失，我們建議提交仲裁。
還能這樣說：
We suggest submitting for arbitration if you don't pay for our loss.
We suggest that the case be submitted for arbitration in the event that you decide not compensates our loss.
應用解析：
suggest有意或無意地讓對方察覺；
hint清楚的暗示，讓對方明白自己的意向；
insinuate以巧妙的方法暗示不愉快或不能明說的事。