I see no reason why your credit score should drop much. I'm on fixed income and maintain high 800 scores. The score is based mainly upon not having late payments etc., and on your credit to debt ratio.
Having credit from very old accounts helps.... so don't close them out ever! It helps show stability plus good credit history.
Having checking and savings accounts also help.
You need to charge things and pay them off at the end of the month. Use each card/account every other month or so if you are paying cash otherwise. Paying cash is not "reportable" and doesn't help credit scores.
Put a stop / filter on your credit bureau accounts that allow only those you've done business with to check your score. Companies "fish" for newbies and they ruin your score, plus the bureaus don't know if you're going to take all those extra card offers... and you're a risk.
Check your credit bureau accounts a few times a year. You can do that freely once a year through freecreditreport.com (I think that's the right addy).... I'm with AAA ProtectMyID and get it all the time, plus Chase banking/cards will let you check it daily or more. Check and dispute any item that you disagree with... even wrong name or address.... you'd be surprised what some people will try to get your credit.
If you have no credit or cards/accounts... open a small savings account and put something into it each week. Once you have enough you can get a bank credit card with a credit line for the amount you have in that savings account. Charge small amounts and pay off each month. After 3 or 4 months of doing this, you will have better credit and might be able to open a regular charge card... and do the same with that charge small amounts and pay off each month; maybe rotate the two cards so they see they are paid off each month.... steady build for credit when there is none.
BEFORE you divorce, open new accounts in your name only, remove your name from spouse's accounts.... this is probably good when aging too... as one of you go first...
There are more tips that help... maybe at SuzeOrman.com ?