I do not recall the timing belt being as SHORT as 60k - a garage might have told you that. BUT, it would not be more than 105k! At 117k, you are on a thread DEPENDING on where you live. Timing belts in the mild weather, humid east coast seem to last very well - my AC belt and Alternator belt on my 95 Ody lasted 100k miles! The dry southwest WILL dry out the belts much sooner.
All this to say, get your belt done soon and you should probably do the cam seals, crank seal and waterpump while you are in there.1999 Honda Odyssey Timing Belt Replacement?This is a job best left to a professional. Don't bring it to the Honda dealer... they will get you for about $800 for parts and labor, including a new water pump. We have a 2000 Odyssey and when the water pump went at 130,000 miles I changed the timing belt. I had a local mechanic do it. He used a rebuilt water pump and 3 hours of labor.... got the whole job done for under $400 with some new gaskets, etc, also. I stopped in and took a look while he was doing the work. The clearances are very tight. This is a large engine in a small compartment. Unless you have a lift, I would not attempt this.
By the way, there is probably no rush to replace this belt. The condition of the belt that I took out of my Odyssey was very good. I felt foolish for doing it but I needed the pump anyway and it just made sense to do it. Most people never get this done despite the risks and most cars do not end up in the junkyard or with massive engine damage since the belt, when it does go, tends to snap on startup before the engine is under load or high rev.1999 Honda Odyssey Timing Belt Replacement?YOU MIGHT NEED TO TAKE IT TO A SHOP THE TIMING BELT COULD SET YOU BACK IF YOU DO IT WRONG BUT IF YOU ARE SKILLED IN THE ART OF TIMEING BELT REPLACEMENT GO FOR IT
IF YOU CAN FIND A SERVICE MANUEL ONLINE