ANSWER: It is true, admittedly, that the Bible never deals with the subject of marriage contracts (prenuptial agreements) with built-in clauses regulating the disposal of assets and the custody of children, etc., in the event of divorce. However, there is a problem with them intrinsically from a Christian viewpoint. Marriage should be lifelong, and the grounds for divorce and remarriage are very narrow when those married are both Christians (e.g. adultery), which is why Jesus gave a warning.
'For this reason a man shall leave his father and mother and be joined to his wife, and the two shall become one flesh'? So then, they are no longer two but one flesh. THEREFORE WHAT GOD HAS JOINED TOGETHER, LET NOT MAN SEPARATE." (Matthew 19)
Although a Christian couple could divorce on other grounds, neither partner could marry anyone else then.
A prenuptial agreement is a built-in way for a couple to marry "with their fingers crossed" when saying, "I do." If a couple makes their commitment to each other CONDITIONAL, then that by itself can help cause what is feared ahead of time and covered in the prenuptial. It shows a lack of commitment to the other partner in such a fundamentally important and intimate relationship to have such mental reservations in advance of committing to him or her. Furthermore, there is always the issue of materialism that must be addressed.
We, as Christians, should not be so terribly upset if half of our assets are lost, if we take seriously what our Savior taught against prioritizing the acquisition of material wealth. Are we put on earth to serve Mammon (money, wealth) instead of God, and to heap up treasures on earth (Matthew 6:19 - 33)? This is a hard thing to say, but it's worth serious consideration even when a man or woman may be very wealthy. We must be willing to let go of what we own if we have to.
So I believe your analysis is correct, that based on the Bible, Christians should not sign prenuptial agreements. This has serious considerations for you personally, which I appreciate. For you are not just looking at this issue as a theoretical issue, but it directly affects your relationship with a man who you have been very seriously involved with romantically. So I wish you well and God's blessing in your decision-making process.