How long should the electronics/relays/etc in an line-interactive UPS last?
You will find it difficult to get an answer to this question because it depends on too many factors. Quality of components used in the UPS, the quality of the manufacturing process, shipping/storage between factory and consumer, handling during installation, environment differences (temperature, airflow, input power quality, etc), and the load generated by the equipment connected to the UPS are just some of the factors that would affect this answer. Any of these factors can vary even between units produced at the same time.
If you ever get someone to give you a clear answer to this question, make sure to check for the fine print. It will likely use some sort of predictive method based on the system design rather than actual data. By the time enough actual data is collected to calculate an accurate lifespan for a UPS model, it will likely have been out of production for some time.
Are there any safety issues, such as increased fire risk from aging electronics?
It would be more accurate to say that there is an increased risk of failure as electronics age, and that failure can potentially result in a fire. However, most failures will not result in a fire.
The exact nature of that failure will be determined by which component(s) fails and for what reason. I have had electronics (both old and new) where components short/burn, ones that simply stop working/fail self tests, and others that start acting "strange" or inconsistently. I personally have yet to see any electronics I am working with fail in a way that starts a larger fire, but the potential does exist.
These are line-interactive units, so the high-power electronics should be seeing no load 99.9% of the time, correct?
Incorrect. When running on AC input power, a line interactive UPS uses almost all of its electrical components; it will use less of them when on DC battery power. Most of the electronics are used for filtering and/or detecting problems with the AC input power. When AC power is present, it still runs through the inverter to both maintain battery charge and provide output power. Power from battery through the inverter is generally considered "clean" and is typically not filtered.
I need to decide if it is time to budget for replacing these UPS, which I would like to delay as long as possible as the replacement cost will be in excess of $35000 USD.
I think this is the heart of your question, even though it isn't phrased as a question. It indicates that your company lacks a replacement schedule/plan/policy for your IT equipment, and every business should have one.
Replacement plans are often driven by one of two types of policy (which may vary depending on type of equipment). Many businesses follow a time based policy. In your case, this could be something like "UPSes are replaced every 8 years." Often this type of policy will be "rolling" in some way (i.e. replace one quarter of the units every other year). Others companies will base their policy on some sort of performance metric. For this example, it may be something along the lines of "we will replace all of the UPSes within two years after product end of life or the first one fails outside of warranty."
The advantage for time based policies is they are simpler for long range planning/budgeting and can help reduce the risk of unplanned downtime due to equipment failure. The trade off is that they tend to have higher capital costs, as you are clearly aware by your statement.
Once your company has a replacement plan, it should make it fairly easy for you to decide when you need to budget the replacement.