Hearthpwn

First of all, you do focus on board control and you usually won't go face until turn 10 or later depending on the enemy's board state. In case you have issues deciding when to clear and when not to clear then just clear until you have lethal you shouldnt have too many problems dealing with common ladder decks except for Freeze Mage maybe. If you are a more advanced player you can feel free to push for dmg and force your opponent into unfavorable trades when your health, board state, and 'taunt situation' allows it.

1. Mulligan for any low drop and gain early board state
2. health is not an issue for you so feel free to jump in face first and drop low on health (except for hunters) while stabilising your board (be careful about wastingConsecrations)
3. once you control the board aim for lethal and force your opponent into unfavorable trades into your taunts 

Mulligans are easy you really only care about getting anything below 4-Mana, and even if you don't get lucky you are usually fine

(without coin): Zombie Chow > Shielded Minibot > Knife Juggler > Muster for Battle > Aldor Peacekeeper > Coghammer

(with coin): Zombie Chow > Shielded Minibot > Knife Juggler > Muster for Battle > Coghammer > Piloted Shredder + (against Hunter/aggro): Antique Healbot Sludge Belcher

I'll just leave you with the winratio screenshot from above, because it speaks for itself you are a control based midrange deck so ofcourse you will suffer from aggro/face decks and im not gonna lie patrons are a pain in the ass as well unless you rly know how to control your Equality + Consecration combo. As you see i barely faced any shamans but in further games i did fine against them its somewhere between 50-70% aswell (btw secret Pallys are getting rekt(ed) hard).

First of all i want to mention you can't replace a card in the purpose it serves, every card is unique in its purpose in the deck. In fact you can adjust your deck in order to improve it against the meta you face or due to financial reasons (Dust).

Concidering this is a common decklist I'll only speak about "controversal" cards and expensive cards which are often asked to replace.

Coghammer - imo one of the most enjoyable cards in the game it's really well designed and serves unique purposes a must include in any Pally deck for me 
replace it with any 2-4 drop of your choice i suggest: Sen'jin Shieldmasta if u feel you need the body with taunt or Argent Lance if u feel like having more weapons

Murloc Knight - "u da MVP" hell this card is awesome it gives you so many late game resources and as you can see on the screenshot above it carries games another enjoyable card to play and really well designed make sure to use it turn 6 or later to get the real power 
no replacement needed as its common

Antique Healbot vs Tuskarr Jouster - my Choice is Antique Healbot due to the reliability he gives you Tuskarr Jouster is way too RNG-based and i hate terrible RNG nevertheless i tried it for 20 games and he either didn't change the situation at all because i was ahead anyway or he just screwed up the entire game and caused me to loose and it's not like +2/2 -1 Health is a big deal in this deck

Quartermaster - i started using just 1 due to financial reasons and i stick with it he gives you a omnipresent threat throughout the entire game and can win you games by turn 4. Still i think using 2 is overkill you just rely too heavily on a good Muster for Battle or you need to wait too long to actually get value out of it
replace it with any 4-6 drop that gives you a certain board pressure as well as tempo to contest control decks, i suggest: Sen'jin Shieldmasta Harrison JonesLoatheb Sunwalker Azure Drake or Mukla's Champion if you like experimenting

Lay on Hands your only actual card draw its an absolute must have otherwise you need to reconstruct the deck with a variation of Azure Drake Guardian of Kings Tuskarr Jouster and similar designed cards.

Tirion Fordring - highest value card in the game and an absolute musthave to contest control decks he determines the entire game he's the one allowing you to just go face and let him run his cards against a wall
If you really need to replace him try any high Mana card that works as a finisher and gains tempo aswell ( i wouldn't adive Ysera nor Nefarian) Try Ragnaros the Firelord or similar cards

there shouldn't be any controversial cards in the common section.