First, you shouldn't be adjusting CR at all, really. CR is a gauge of monsters "power". Ogres are CR2 due their "power" (ie hP, DPR, etc) if you adjust CR you are adjusting its HP, its DPR, its to hit modifier etc...in short, it stops being an Ogre (maybe ogre child, or Sick ogre) but then you are changing the narrative in the module. You can fudge it a bit (lower/raise to hit by 1 or 2, damage by 2-4, hp by some percent etc) and be ok, but there are too many moving parts to judge well to really come up with a new CR. As a rule of thumb -1 on attacks, -2 on damage and about 75% HP are probably good for a small party but...encounter difficulty is a function of "effective" XP budget, and multiple monsters are LARGE driving force in that determination. Smaller groups are key for smaller parties
Second, in a published adventure you are likely not going to see a CR > Party Level except in extreme/specific circumstances. So any creature presented should be "viable" for a smaller group as presented.
So, the best way to adjust encounter difficulty is reduce the number of monsters and/or number of encounters.
For HotDQ, I'd drop number of monsters in half. If you roll on a table and get 1d6 Kobolds, make it 1-3. If a set encounter has 6 kobolds and 4 cultists, make it 3 and 2, etc. I'd also use the average damage listed rather than roll. Random is spikey, and in a small party 2 random high damage rolls can drop 2/3 of your party, where in a larger party more than 1 guy is still standing. Average will help you pace as well. As DM you can see if your average damage means any hit kills a PC. If so, you might switch to more robust targets, or start having creatures run, or reinforcements arrive, etc.
In my own home run HotDQ, Im a using Average Damage -2 at 1st level, Average -1 when they hit 2nd, Average at 3rd, then Rolling from then on at 4th+. They are still getting their butts kicked at 1st level and after 2 sessions, are rolling backup characters, lol! We'll see. (4 PCs)
In the encounters session HotDQ I am running, I have 7 players. Since many are new to D&D, New to the system, Or very young, I won't increase number of creatures and I still think I'll use Average Damage -2 at 1st level, Average -1 when they hit 2nd, Average at 3rd, then rolling from then on at 4th+. I may change my mind if the first 2 or 3 encounters go too well for them.
Have fun and Good Luck!