I'm a 66 year old, 6 ft 3 inch (190cm) 18 and 1/2 stone (117kg / 259 lb) biker !
I own a cannondale carbon synapse with a 32 tooth cassette on the rear wheel that was okay for Mont Ventoux climb last year. This year our group of skinny bikers ( I'm the heaviest by 4 stone) are planning all the passes in the Lake District over 4 days.
Can I put on a 36t cassette without changing all the front chainrings and chain as long as I keep the same number of cogs on the rear cassette i.e. 8?
Presuming you have a double, the simple way of doing it that doesn't involve changing out everything is using one of these or something similar. You'll need a new chain to be able to wrap around the large/large combo safely if you wind up in that gear by accident. And, the drawback of this route is that you're increasing the large cog clearance but not the total capacity, meaning once the chain is long enough to run the new cassette safely, the derailer probably won't have the ability to tension the chain in the small/small combos (you can figure out which ones by looking up the exact total capacity of your rear derailer). If you go that route, make sure to read all the instructions on the linked page to make sure it all looks good with what you have.
You don't say what components you have, double or triple, and number of rear cogs. All of that has a lot of bearing on what the other options would be. Basically there are ways of getting a mountain rear derailer on your right shifter, which would then natively have both the total capacity and the large cog clearance you want, but steps required to do that depend on those factors.
These are serious climbs:
Not high, but hard, some with gradients of 25% and even 33%
Kudos for Mont Ventoux. It's long, but the gradients come nowhere near these climbs!
For such climbs, you'll want the lowest gearing you can possibly get. If your front rings are the stock compact 50/34 ones then the 38 rear you are considering is a good idea.
But if you have the Shimano 105 5800 GS rear derailleur (or similar), then you're out of luck, because 32 teeth is the most it can handle.
So, you'll be needing either
The next thing is training. Although you didn't ask here are my suggestions ... but firstly the good news ... hauling your body mass up a hill like Mont Ventoux means you have a serious level of strength and fitness. The key is to loose some of the mass while keeping the strength and endurance.
From my observations for most males (it doesn't work the same for females) the best thing for weight loss is a 40 minute training ride before breakfast. To maintain strength, do hill repeats or efforts on gradients of 8 to 15% Find a steep and climb it once a month to track progress. Mix these rides with Long Slow Distance rides to maintain aerobic condition. Be careful not to overtrain; 3 rides per week is enough.
I'm sure you don't need advice for the actual climbs, but for others who read this, such climbs should be started slowly, they get hard enough soon enough!
Enjoy!
Short answer: no.
Since you're adding 4 more teeth on the big cog, then your chain will need to be 4 half-links longer when on the big-big combination. This may leave your chain too long for the small-small combo.
If your chain has a quicklink then undo it, cut and fold a wire or old spoke into a double hook that is as long as 6 half links, and temporarily extend your chain by hooking it over the rollers. (its 2 more because removing the quicklink essentially takes 2 other links out) Don't ride like this, just do a visual check of small/small.
Another problem is your B screw and whether the 36 tooth large cog will clear the teeth. The only way is to eyeball the current large cog and use your hand to push the derailleur to the rear, while imagining "one larger cog" and see if it will fit.
If you replace your cassette/block then you should fit a new chain. You could keep the old chain with the old cassette if you want to revert.
Finally - don't take this the wrong way, but you're carrying penalty weight. Consider carrying as little gear as possible up the climb. Off load as much gear as you can to any support car.
