You replace something - as opposed to repair- you get to meet the new code rules.
Newer code specifies a 100-amp minimum service disconnect. The old, round meter bases are rated fro 60 amps. Therefore, you need to replace the meter base.
100 amps requires larger wire than 60 amps, and the PoCo standards may mandate a 2" minimum riser anyway. Remember- with a service change, the local PoCo is the AHJ, and you need to work with them.
You mentioned "insurance company" requirements. Perhaps I can shed some light on this topic.
I have obtained parts of a 'claims manual' from one insurance company. (If you ever saw "The Rainmaker," you have some idea of the significance of this manual). Now, before you dither about each company being different, you have to know that the manual refernces "Insurance Institute" standards. Yes, they have their own, confidential, trade association rules. These rules are, in turn, often determined by various legal actions, so an individual carrier is not likely to vary much in the application of the rules.
Simply, put, there are different 'levels' of homeowners' insurance. The criteria used to classify a property addresses many things, some completely unrelated to the property itself.
Past a certain age - 40 years is one figure- insurance companies don't just say 'we want breakers.' What they actually ask is: were the utilities (plumbing, sewer, electrical, etc.) ever brought up to a more recent code? If so, by whom and when? In practical terms, this means the underwriter is going to be looking for a 100-amp meter base and breakers. Simply swapping out fuses for breakers - there are screw-in breakers made for this- won't make the agent happy. Nor will simply swapping out panels. He wants to see that some real work was done, by someone who knew what he was doing.
Another element is grounding. Many old places do not have any ground besides the water bond; this isn't enough. The agent is looking for that ground rod, too.
It's a pity the insurance industry is so secretive about these things. They seem to have this belief that sharing information will result only in misunderstanding and fraud. So, they are taught to never actually answer a question. They're not about to give you a 'punch list' of things you can do to improve your rates and your coverage.
Your customer also needs to know something else: after having a policy for a year, they will likely be able to get a better, cheaper policy from another firm. What improvements they make during that year has a major effect on that possibility. Do the least possible, and you'll be stuck with the worst possible coverage and the highest rates.