I took that TECEP and passed without studying at all. Yes, the Handbook you have will be fine. They haven't updated the APA or MLA formats since 2009, so anything after that is good.
I borrowed a Hodges Handbook from my local library, put post-it notes on the sections listed in the study guide, and did just fine. You're probably way more prepared than I was (although honestly, I didn't think taking the test was anywhere near as hard as a class would have been).
TESU BSBA in HR (in progress) - 108cr, only 4 more classes to go...
GGU Certificate in Management - 2000
TECEP - Technical Writing 84% (3cr), English Comp II 79% (3cr), Applied LibArts Math 90% (3cr), Public Relations 70% (3cr), Computers 75% (3cr) DSST - Intro to Computers/437 (3cr), Prin of Pers Finance/458 (3cr) - 2011 CLEP - Management/69 (3cr UL), Marketing/67 (3cr UL) - 2011
Penn Foster - Financial Management 92% (3cr UL) ALEKS - Int Alg (3cr) - 2011, College Algebra (3cr) - 2015 Sophia - Project Management 85% (3cr UL) - 2015 Insurance Inst. of America - Ethics 72% (2cr) - 2015 Kaplan PLA (3cr) - 2015 Add'l ACE Credits (5cr UL) - 2000
Palomar College - Organizational Theory (3cr) - 2015 Mission College (36cr) - 92-98 Golden Gate Univ (12cr UL, 3cr LL) - 98-00 San Jose State Univ (12cr UL, 9cr LL) - 88-89