Hello!
There is! Mesmers in PvE often rely on their phantasms for a good chuck of their damage. You have the choice of a greatsword, pistol, focus, or off-hand sword: these all have a powerful phantasm on their bar. With a sword in your main-hand as well, you have access to a good hard-hitting skill which lets you evade at the same time.
It's hard to play GW2 without a mouse, I'd really advice against it. It's downright impossible for PvP and very very impairing in PvE. For your keyboard situation: I'd say at least make sure you can effecively use skills #1 through 5 with your left hand. They have to be activated quite often.
So to conclude: yes, you could theoretically play without a mouse, but it's a nuisance. It doesn't help that you like two professions with a lot of skills (mes and engi), but between those you chose the least skill intensive.
Ill post some PvE mesmer stuff here if you're interested:
You might notice that your damage output is quite low and you don't take a lot of hits. Try using a Greatsword/Staff to stay at range (they both have pretty decent skills, but the GS has more damage) and use a sword in your main hand for your other weapon set (you can swap between weapons after a few levels). Skill 2, Blurred Frenzy does good damage and evades all attacks for 2.5 seconds! You can choose either of the three off-hands I listed above, with each their own benefits. Pistol can summon a powerful phantasm that attacks from ranged, the sword offers a more melee-based phantasm (so it might die faster) and has a block attack. The focus offers a melee phantasm that whirls around and absorbs projectiles while doing good damage. This one is very useful against ranged foes. Your skill #4 creates a line that gives swiftness when you walk through it and cripples enemies (so you can create some distance between you and your foe) and can then also pull foes towards that line.
To stay alive, make sure you use your dodge ability, stay ranged or block and negate damage using the skills I mentioned above. The mesmer requires quite some skill to play well.